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Digitized  by  the  Internet  Archive 

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http://www.archive.org/details/cumulativeharmonOOmccoiala 


CUMULATIVE  HARMONY 


BY 

WILLIAM  J.  McCOY 


GINN  AND  COMPANY 

BOSTON     .    NEW   YORK     •    CHICAGO     •    LONDON 
ATLANTA     •    DALLAS    •    COLUMBUS     •    SAN    FRANCISCO 


k  1  8 


COPYRIGHT,  1916,  BY  WILLIAM  J.  McCOY 

ALL   RIGHTS   RESERVED 
516.7 


ttfte  gtftemmm   gre«< 

GINN  AND  COMPANY  •  PRO- 
PRIETORS •  BOSTON  •  U.S.A. 


LIBRARY 

I 
'J 


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PREFACE 

Inasmuch  as  there  are  already  available  textbooks  on  harmony,  a 
title  list  of  which  would  form  an  imposing  array,  and  among  which  may 
be  noted  a  number  of  thoroughly  sound  and  admirably  constructed 
works  by  American  theorists  of  distinction,  the  question  would  natu- 
rally arise.  Why  add  another  ? 

The  greatly  deplored  apathy  of  music  students  toward  the  study  of 
harmony  is  largely  due  to  the  fact  that  harmony  methods,  in  general, 
are  prepared  for  mature  minds,  which  are  often  too  much  engrossed 
with  an  already  acquired  proficiency  in  executive  music  to  welcome 
readily  the  thorough  course  that  is  necessary  in  order  to  absorb  the 
apparently  inelastic  mass  of  facts  presented,  which,  they  subsequently 
discover,  requires  a  supplementary  course  to  determine  definitely  its 
mission  in  music  practice. 

It  has  been  the  earnest  effort  of  recent  theorists  so  to  modify  the 
prevailing  modes  of  procedure  that  a  more  kindly  attitude  toward  this 
subject  may  be  encouraged. 

It  is  with  this  object  in  view  that  the  author,  through  many  years  of 
experience  in  teaching,  has  evolved  a  course  in  chord  practice  by  means 
of  which  the  problem  of  covering  thoroughly  all  phases  of  the  science 
of  harmony  and  at  the  same  time  creating,  on  the  part  of  students,  a 
direct  interest  in  the  subject  for  itself  has,  he  believes,  been  success- 
fully solved. 

By  means  of  the  plan  here  presented,  the  student  is  led,  step  by 
step,  through  the  process  of  theory  and  practice,  and  becomes  himself 
a  party  to  the  building  up  of  the  system. 

The  work  is  made  continuously  cumulative.  As  each  new  unit  is 
added  it  enters  at  once  into  the  practice  of  music-making,  and  con- 
tinues in  homogeneous  action  until  the  entire  work  is  absorbed. 

Melody-making  (as  a  superstructure)  from  harmonized  given  bass 
sets,  and  the  harmonization  (as  a  substratum)  of  given  melodies,  are 
introduced  almost  at  the  outset  and  continued  with  constantly  cumu- 
lated harmonic  elements  through  the  work. 

The  forming  of  melodies  from  combined  harmonic  units  is  regarded 
by  the  author  and  those  who  have  practiced  this  method  as  a  most 


iv  CUMULATIVE  HARMONY 

valuable  innovation  ;  by  this  means  the  enlistment  of  creative  effort 
becomes  at  once  a  source  of  fascination  to  the  student,  which,  as  new 
chords  are  involved  and  his  own  efficiency  becomes  greater,  increases 
continuously  throughout  the  course. 

The  author  desires  to  direct  attention  to  the  following  innovations 
peculiar  to  this  work  : 

1.  The  evolving  of  melodies  from  harmonic  structures. 

2.  A  tabulated  system  of  modulation  to  directly  related  keys,  con- 
sidered harmonically  and  melodically. 

3.  A  recognition  of  this  principle :  the  fact  that  the  positive  identi- 
fication of  a  key  is  dependent  upon  an  assured  Dominant  chord  is 
sufficient  justification  for  assuming  that  the  appearance  of  such  chord, 
in  any  circumstance,  serves  fully  to  identify  a  key. 

4.  The  harmonization  of  melodies  by  the  three-point  mode,  involv- 
ing the  grouping  of  all  chords  into  three  general  harmonic  families,  by 
means  of  which  a  freedom  in  authoritative  harmonization  of  given 
melodic  lines  is  easily  acquired. 

5-  The  use  made  of  the  secondary  chords  of  the  Subdominant, 
Tonic,  and  Dominant,  regarding  which  the  author  asks  only  that  those 
who  may  already  have  acquired  a  working  knowledge  of  chords  as  based 
upon  all  degrees  of  the  scale  will  give  to  this  mode  of  grouping  for 
harmonization  of  melodies  a  thorough  consideration  entirely  disassoci- 
ated from  and  unprejudiced  by  the  edicts  of  former  affiliations,  in  order 
to  become  convinced  of  its  simplicity  and  superior  practicability. 

The  author  is  confident  that  a  careful  contemplation  of  the  family 
of  augmented  chords  as  presented  in  this  work  and  verified  by  the  ac- 
companying illustrations  will  easily  disperse  the  "  bogy  "  mysteries  with 
which  this  chord  has  been  persistently  surrounded. 

The  study  of  harmony  should  be  pursued  simultaneously  with  the 
study  of  instrumental  and  vocal  music.  It  should  be  thoroughly 
mastered  and  absorbed  during  the  receptive  periods  of  childhood  and 
youth,  not  deferred  until  the  musical  character  has  been  already 
formed  and   new  lines   of  thought  become   unwelcome. 

This  textbook  is  an  offering  of  method  and  material  from  which  the 
instructor  and  the  pupil  are  expected  to  develop  a  wide  scope  of 
musical  study  that  will  prove  a  true  preparation  for  other  steps  toward 
analysis  and  composition. 

WILLIAM  J.  McCOY 


CONTENTS 

CHAPTER  PAGE 

I.  Notation i 

Scales I 

Major  diatonic  scale 2 

Relative  minor  diatonic  scale 3 

Tonic  minor  scale 4 

II.  Intervals 7 

General  name  of  intervals 7 

Specific  name  of  intervals 7 

Inversion  of  intervals 12 

Consonant  intervals 13 

Dissonant  Intervals 14 

III.  Chords 16 

Triads 16 

Major  triad 16 

Minor  triad 16 

Augmented  triad 17 

Diminished  triad 17 

IV.  Harmonization  in  Four  Voices  over  a  Given  Bass 19 

Progression  of  voices 19 

Similar  motion 20 

Contrary  motion 20 

Oblique  motion 20 

Transposition 21 

Compass  of  voices 22 

V.  Inversion  of  Triads 24 

Fundamental  position 24 

First  inversion 24 

Second  inversion 24 

Figured  bass 25 

VI.  The  Construction  of  Melodies  over  Accompaniments.     ...  31 

Accompaniments 34 

VII.  Parallel  Fifths  and  Octaves 40 

VIII.  The  Do.viinant  Seventh  Chord 43 

Resolution  of  the  D^  chord 44 

Table  of  resolutions 45 


vi  CUMULATIVE   HARMONY 

CHAPTER  PAGE 

IX.  Inversions  of  the  D''  Chord 48 

First  inversion 48 

Second  inversion 48 

Third  inversion 50 

X.  Serial  Modulations 53 

/               Rule  I.    Tonic  for  new  Dominant 54 

Rule  II.    Supertonic  for  new  Dominant 56 

Rule  III.    Mediant  for  new  Dominant 57 

XI.   Serial  Modulations  (Continued) 59 

Rule  IV.    Subdominant  for  new  Dominant 59 

Rule  V.    Submediant  for  new  Dominant 60 

Rule  VI.    Subtonic  for  new  Dominant 60 

XII.  Directly  Related  Keys 63 

XIII.  Harmonization  of  Melodies 66 

Rule  I 66 

Rule  II f  .     .     .     .  69 

Rule  III 69 

Rule  IV 70 

XIV.  Harmonization  of  Melodies  (Continued) 73 

Rule  V 73 

XV.  Harmonization  of  Melodies  (Continued) yy 

Melodies  employing  inversions 77 

Consideration  of  the  £  chord 78 

The  abbreviated  D^  chord  D) 80 

XVI.  Secondary  Chords  on  the  Subdominant 83 

Subdominant  substituted  6th  chord 83 

Subdominant  added  6th  chord 84 

Rule  VI  for  harmonization  of  melodies 86 

Dominant  of  the  Dominant  in  passing  modulation 88 

XVII.  Melodic  Modulation 93 

Rule  I 94 

Rule  II 95 

Rule  III 96 

Rule  IV 97 

Rule  V 98 

Rule  VI • 99 

XVIII.  Embellishments 103 

Suspensions 103 

Rule  I 106 

Rule  II 107 

Rule  III 109 

XIX.  Suspensions  (Continued) iio 

Rule  IV no 


CONTENTS 


Vll 


CHAPTER 
XX. 


XXI. 


XXII. 


XXIII. 


XXIV. 


XXV. 
XXVI. 


XXVII. 
XXVIII. 


XXIX. 
XXX. 


Retardations,  or  Ascending  Suspensions 

Rule  I 

Rule  II 

Rule  III 

Rule  IV 

Passing  Notes 

Successive  passing  notes 

Consideration  of  the  various  forms  of  the  minor  scale     .     .     . 

Compound  passing  notes 

Chromatic  Passing  Notes 

Germ  set  and  motus 

Extended  passing  notes 

Auxiliaries 

Successive  auxiliaries 

Extended  auxiliaries 

Introductory  Auxiliaries 

Progressive  auxiliaries 

Changing  notes 

Anticipation 

False  relation 

The  Dominant  Ninth  Chord 

Additional  rule  for  harmonization  of  melodies 

The  Abbreviated  Dominant  Ninth  Chord  D))    .     .     .     . 

Rules  for  treatment  of  D))  chord         

Additional  rule  for  melodic  modulation    ........ 

Diminished  7th  chord 

Additional  rule  for  passing  modulation 

Imitation 

Imitation  in  two  voices 

Cadences  

Complete  cadence ;     .     .     .     . 

Authentic  cadence 

Plagal  cadence 

Tierce  de  Picardie 

Incomplete  cadence 

Deceptive  cadence 

Passing  cadence 

Extended  Cadences  

Extraneous  Modulation 203 

Indirectly  related  keys 204 

Foreign  keys 207 

Transition 209 


23 
24 
26 
29 

32 
32 
33 
36 
40 
41 
48 
50 
52 
52 
53 
62 
65 
70 
70 
73 
74 
75 

85 
87 

9' 
9' 
91 
94 
95 
96 

97 
98 

99 


# 


viii  CUMULATIVE   HARMONY 

CHAPTER  PAGE 

XXXI.  Secondary  Chords  on  the  Tonic 211 

Tonic  substituted  6th  chord 211 

Deceptive  cadence  involving  the  Tonic  substituted  6th  chord     .  212 

XXXII.  The  Toxic  Added  Sixth  Chord  TJ 216 

Additional  rule  for  harmonization  of  melodies 219 

Dominant  of  the  supertonic  in  passing  modulation 219 

XXXIII.  Composition  of  Chorals 223 

XXXIV.  Chromatic  or  Altered  Chords 224 

Augmented  6th  chord 224 

French  6th  chord 225 

Italian  6th  chord . 227 

German  6th  chord 228 

Modern  augmented  6th  chord 229 

XXXV.  The  Neapolitan  Sixth  Chord 234 

XXXVI.  Augmented  Fifth  Chords 238 

Additional  rule  for  harmonization  of  melodies 242 

XXXVII.  Imitation  over  Given  Fundamentals 245 

Imitation  in  three  voices 247 

XXXVIII.  Additional  Embellishments 250 

Arpeggios 250 

Direct  arpeggios 250 

Indirect  arpeggios 250 

Chromatic  scale  passages 252 

Ornamental  anticipations 255 

XXXIX.  Irregular  Resolutions  of  the  D''  Chord 258 

XL.  Secondary  Chords  on  the  Dominant 264 

Dominant  substituted  6th  chord 264 

Additional  rule  for  harmonization  of  melodies 264 

Dominant  substituted  6th  chord  with  7th  included 266 

XLI.  Dominant  Added  Sixth  Chord 271 

XLII.  Chords   of   the   Tonic   Seventh   and   the   Subdominant 

Seventh 278 

Table  of  direct  and  tributary  chords 282 

XLIII.  Sequences 287 

Pedal  Point 290 

INDEX 297 


CUMULATIVE   HARMONY 

CHAPTER   I 
NOTATION 

Notes  are  written  symbols  representing  tones  (musical  sounds)  to 
be  uttered  by  the  human  voice  or  other  medium  of  musical  expression. 

The  terms  "  steps  "  and  "  half  steps  "  are  used  as  a  medium  of 
reference  to  the  difference  in  pitch  of  varying  tones.  By  a  half  step 
is  meant  the  distance  (difference  in  pitch)  from  any  one  note  to  the 
nearest  note  in  general  use  above  or  below  it. 


1        }^  step  }4  step 


j^  step  }^  step  }y^  step  }^  step 


'■'—^9 ^ 


I 


:^ 


-fc>?g — bar- 


--^ 


^-     %-^ 


The  distance  of  two  combined  half  steps  constitutes  a  whole  step 
(or  a  step). 


step 


g 


•«-  I 


fn 


>^step 


y^ 


step 


step 


step 


n:: 


*^ 


hd23 


X 


% 


Scales 


-^9^- 


% 


I 


I 


The  plans  of  scales  used  in  various  periods  and  by  various  peoples 
differ  materially.  For  a  description  in  detail  of  the  many  forms 
that  have  been  employed,  the  student  is  advised  to  refer  to  a  suitable 
history  of  music  and  become  fully  informed  on  this  very  important 
subject. 

Attention  will  be  directed  for  the  present  to  the  major  and  minor 
diatonic  scales. 

I 


CUMULATIVE   HARMONY 


Diatonic  is  the  name  given  to  music  that  conforms  entirely  to  the 
immediate  tonality  or  key  in  which  it  occurs,  as  would  be  indicated 
by  the  signature  of  that  key. 

It  also  refers  to  a  series  of  such  notes  proceeding  by  degree  in  one 
direction. 

3     Diatonic 


■i==t 


--=t 


^ — ^ 


4      Not  diatonic 


i 


i^ 


=]: 


i 


*^S^ 


:«^ 


A  scale  is  a  series  of  eight  tones  at  distances  of  a  whole  or  a  half 
step  apart,  as  represented  by  corresponding  notes  upon  contiguous 
degrees  of  the  staff.  i 


i 


^ 


E#=^ 


:f= 


The  eighth  note  in  this  series  —  which  is,  in  reahty,  a  duplicate  in 
the  octave  of  the  first  —  not  only  serves  as  the  last  of  the  series  in  one 
scale,  but  may  constitute  at  the  same  time  the  first  in  the  next  scale 
series  above. 

8 
6 


i 


I 

2      3      4       5     Li..:^     A  = 


*-— ^ 


F& 


_^_^ 


w^. 


^- 


#-^ 


etc. 


Ji=±: 


<^-      ^      3       4       5       6       7 


1         2      3 


The  diatonic  scales  are  in  two  genders  —  the  major  and  the  minor. 


The  Major  Diatonic  Scale 

The  succession  of  whole  steps  and  half  steps  separating  the  eight 
members  of  the  major  diatonic  scale  is  as  follows  :  a  whole  step  be- 
tween each  two  contiguous  notes  except  between  three-four  and 
seven-eight,  which  are  a  half  step  apart. 


NOTATION 


A  major  diatonic  scale  beginning  with  the  note  C  would  appear  in 
whole  step  and  half -step  distances,  as  follows: 


i 


step  step  }^  step  step  step 

i ^1    I 1    1 1    I 1    I 1    I 


I 


2^ 


-^2345678 

Beginning  with  F  and  with  D,  similar  scales  would  appear  as  fol- 
lows: 

8  step  step  }4  step        step  step  )^ 

I  I      I  I    i  ^1    (  I    I  I    I  i    1 1 


* 


2  3  4  5  6  7  8 

step  step  %  step  step  step  }^ 


$ 


~i    I 1     I 1    I 1     r 


^fe— g— ^ 


--^ 


-zt- 


The  Relative  Minor  Diatonic  Scale  (Normal) 

This  scale,  with  the  same  signature,  is  located  two  staff  degrees  be- 
low the  major,  and  occurs  in  the  following  succession  of  steps  and 
half  steps:  a  whole  step  between  each  two  contiguous  notes  except 
between  two-three  and  five-six,  which  are  a  half  step  apart. 

A  minor  diatonic  scale  beginning  on  A  would  appear  as  follows, 

10  step  }^  step  step  "%  step  step 

\ 1    I 1    I 1    I 1    1 1    I 1     I 1 


I 


4: 


'li^.  '^  ''^  A  5  6  7 

and  similar  scales  beginning  on  D  and  on  F#,  as  follows: 

11  step  y^  step  step  )^  step  step 

I 1    I 1    1 ^1    I 1    I 1    . 1     I 


i 


J    .i    i    "'   "'    r    I — " 


CUMULATIVE   HARMONY 


12 


step 


step  step 


step 


step 


1 


XT 


2 


--P^ 


12  3  4  5  6  7  8 

Here  follow  two  excellent  illustrations  of  the  employment  of  the 
Normal  Minor  Scale. 


Illustration  No.  1 


P^^ 


t=i 


Schubert,  "  Symphony  B  Minor" 


% 


-Jt4— ^— - 


^^^ 


:=1= 


111.  No.  2 


n   u       Alleg70  moderaio 


Mrs.  H.  H.  A.  Beach,  op.  45,  "  Concerto" 


ij: 


^ 


-(&- 

//  ^ 


-^^ 


^"^ 


^ 


^^ 


^^i^ 


m^ 


r^ 


^^^^-. 


irisi5 


-25*- 


This  scale  is  subject  to  alterations  due  to  certain  harmonic  and 
melodic  conditions,  which  will  be  considered  later. 

The  Tonic  Minor  Scale 

The  form  of  the  diatonic  content  of  the  tonic  minor  is  identical 
with  that  of  the  relative  minor;  but,  while  the  tonic  of  the  relative 
minor  is  a  third  below  the  tonic  of  the  major,  that  of  the  tonic  minor 
is  the  same  note  as  in  the  major.  The  tonic  minor  scale  of  the  key 
of  C  major  is  as  follows: 


13 


step 


^^ 


step 


step 


step 


step 


i 


iS 


-O- 


I 


The  technical  names  of  the  various  members  of  the  diatonic  scale 
are  as  follows: 

The  first  of  the  scale  is  called  the  Tonic;  the  second  of  the  scale 
is  called  the  supertonic;  the  third  of  the  scale  is  called  the  mediant; 
the  fourth  of  the  scale  is  called  the  Subdominant;  the  fifth  of  the 
scale  is  called  the  Dominant;   the  sixth  of  the  scale  is  called  the 


NOTATION  5 

submediant ;  the  seventh  of  the  scale  is  called  the  subtonic  or  leading 
tone;    the  eighth  of  the  scale  is  called  the  octave  or  Tonic. 

Of  these  the  Tonic  [T],  Subdominant  [S],  and  Dominant  [DJ  are 
classed  as  primary  notes,  the  others  as  secondary. 

A  diatonic  scale  may  be  formed  with  any  note  as  the  Tonic,  or  key- 
note. 

In  order  to  aid  the  student  in  becoming  familiar  with  the  suc- 
cession of  sharps  and  flats  placed  in  signatures  to  form  and  indicate 
the  various  keys  and  scales  in  general  use,  two  rules  are  submitted  : 

From  the  key  of  C  major  with  a  signature  of  no  sharps  or  flats, 
proceeding  by  sharps: 

Sharp  the  fourth  and  take  the  fifth  for  a  new  Tonic,  or  keynote. 


14  % 


y^ 


With  the  fourth  [F]  sharp  and  the  fifth  [G]  as  the  new  Tonic,  or 
keynote,  a  signature  of  one  sharp  and  the  key  of  G  appears. 
15  M  % 


i 


>-■ — ^— .f=.*=^=^='«'f=^ 


From  the  key  of  G  with  the  fourth  [C]  sharp  and  the  fifth  [D]  as 
the  new  Tonic,  or  keynote,  a  signature  of  two  sharps  and  the  key 
of  D  appears. 

Proceeding  by  flats: 

Flat  the  seventh  and  take  the  fourth  for  a  new  Tonic,  or  keynote. 

16  u  u 


g 


-z:)- 


--m 


^ 


With  the  seventh  [B]  flat  and  the  fourth  [F]  as  the  new  Tonic,  or 
keynote,  we  have  a  signature  of  one  flat  and  the  key  of  F. 

17  _J£^  ^J£^ 


i 


:^ 


:(12)^ 


I 


In  like  manner,  with  the  seventh  flat  we  have  the  key  of  Bb  with 
two  flats  in  the  signature. 


6  CUMULATIVE   HARMONY 

A  thorough  familiarity  with  the  various  keys,  as  indicated  by  their 
signatures,  is  a  necessity  at  this  point  in  the  student's  work,  and  con- 
siderable oral  drill  should  be  given  in  the  manner  of  the  following 
patterns: 

Note.  References  to  the  Tonic,  or  keynote  of  tonalities,  will  be  made  by  symbolized 
capital  letters  for  the  major  keys,  and  symbolized  small  letters  for  the  minor ;  thus :   C 

A  .  ^  .  ^  ^ 

major,  C  ;  A  major,  A ;  F  minor,  f ;  D  minor,  d. 

Give  the  signatures  in  as  rapid  succession  as  possible  of  the  follow- 

A        A        A        A        A  A        A 

ing  major  keys:   G,  F,  D,  E,  Bb,  A,  Eb,  etc.     Give  the  signatures  of 

A.Aa.A  .  A  A 

the  following  minor  keys:  d,  a,  b,  g,  e,  d#,  g#,  eb,  f#,  etc.  Name  the 
major  keys  represented  by  the  following  signatures:  i  flat,  3  flats,  3 
sharps,  2  flats,  5  sharps,  etc.  Name  the  minor  keys  represented  by 
the  following  signatures:  i  sharp,  3  fiats,  4  sharps,  5  flats,  2  sharps,  etc. 

Chromatic  alteration  is  a  term  used  in  raising  or  lowering  a  note  a 
half  step  by  means  of  an  accidental  sharp,  flat,  or  natural  other  than 
those  established  by  the  signature.  Chromatic  alterations  may  raise 
or  lower  the  pitch  of  notes  without  causing  a  change  of  key,  or  they 
may  aid  in  effecting  modulations.  When  a  note  is  raised  by  means  of 
an  accidental,  it  is  said  to  be  elevated;  when  it  is  lowered  by  the  same 
means,  it  is  said  to  be  depressed. 

By  chromatic  progression  (or  motion)  is  meant  the  proceeding  from 
one  note  to  another  a  half  step  higher  or  lower.  This  may  be  ac- 
complished with  or  without  chromatic  alteration. 

^^         (a)     {b)        (c) 


^=p 


At  (a)  is  a  chromatic  progression  without  chromatic  alteration;  at 
(b),  (c)  chromatic  progressions  formed  with  the  aid  of  chromatic  alter- 
ations.    The  progression  at  (a)  is  also  diatonic. 

The  student  should  frequently  play  and  have  played  for  him  the 
scales,  both  major  and  minor,  in  all  keys.  The  same  may  be  said  of 
all  examples  and  exercises  throughout  the  course  of  study  as  they 
occur  and  are  worked  out.  It  is  a  matter  of  the  utmost  importance 
that  attention  be  given  to  frequent  playing,  hearing  played,  and  an- 
alyzing all  examples  and  exercises  as  they  occur  and  are  worked  out. 


CHAPTER   II 


INTERVALS 

An  interval  consists  of  two  tones  (or  the  difference  in  pitch  of  two 
tones  as  determined  by  the  corresponding  notes  on  the  staff)  to  be 
heard  simultaneously  or  in  succession.  Intervals  are  computed  up>- 
ward  from  the  lower  note. 

The  general  name  of  an  interval  is  determined  simply  by  the  number 
of  staff  degrees  involved. 

19         prime  2d  3d  5th 


i 


p 


etc. 


:1=t 


-<5^ 


f-r 


one  degree  two  degrees  three  degrees  five  degrees 

Intervals  greater  than  an  octave  are  given  the  same  interval  names 
as  similar  ones  within  the  octave,  and  the  octave  itself  is  treated  as  a 
duplicate  of  the  lower  note  at  a  higher  altitude. 

2d  4th 


20    2d 

/I 


rS 


4th 


T 


etc 


The  specific  name  includes,  also,  an  estimate  of  the  number  of  steps 
and  half  steps  the  interval  contains. 


21 


augmented  prime 


minor  3d        major  3d  perfect  4th 


%  Step 


-l>(S>- 


3z: 


etc. 


\%  steps        2  steps 


1%  steps 


Taking  C  for  the  lower  note,  the  specific  intervals  obtainable  with- 
out chromatic  alteration  are  the  perfect  prime,  fourth,  fifth,  and 
octave;   the  major  second,  third,  sixth,  and  seventh. 

22      prime  fourth  fifth  octave 


i 


prime 


-«»- 


3?: 


I 


Perfect 


CUMULATIVE   HARMONY 


23 


3d 


6th 


7  th 


i] 


Major 


From  the  examples  above  the  student  may  learn  that  the  two 
notes  forming  a  perfect  prime  are  similar  in  all  respects,  the  one 
being  a  dupHcate  of  the  other,  on  the  same  staff  degree;  that  the 
two  notes  forming  a  perfect  fourth  are  two  and  a  half  steps,  and  a 
perfect  fifth,  three  and  a  half  steps  apart;  and  that  the  upper  note  of 
a  perfect  octave  may  be  seen  to  be  a  duplicate  of  the  lower,  in  the 
octave.  Also  that  a  major  second  contains  one  step,  a  major  third 
two  steps,  a  major  sixth  four  and  a  half  steps,  and  a  major  seventh  a 
half  step  less  than  an  octave. 

The  student  will  now  form  and  write  perfect  fourths  upon  each 

A 

note  of  the  scale  of  C;  also  upon  its  depression  and  its  elevation,  thus: 


24 


Perfect  4ths 


:^-%|*i=if^ 


etc. 


Form  and  write  perfect  fifths  similarly, 

25 

Perfect  5ths 


Form  and  write  in  like  manner,  successively,  major  seconds,  thirds, 
sixths,  and  sevenths. 


:i 


26 

Major  2ds 


W- 


^^^ 


-z^ 


—^^- 


g>^ 


i 


W^5=^^^^^— 


iiS=i 


is^"!^' 


27 


g 


Major  3ds 


''Tsy^- 


W 


m 


-^- 


-ts- 


etc. 


iX^ 


etc. 


INTERVALS 


^ 


28 

Major  6ths 

f-ir-L 


W 


-/C!       <». 


fK 


20 

Major  7ths 


s» «»- 


g 


etc.    /C     t>Ji!g 


^-^t>5^fi- 


etc. 


-xisr 


1^^^=^ 


i|2=^^  etc.  ^^J=^=^ti: 


-s^ — fi^ 


t2=^=^^^^ 


etc. 


etc. 


The  distance  of  a  minor  interval  is  a  chromatic  half  step  less  than 
that  of  the  major. 

Form  and  write,  successively,  minor  seconds,  thirds,  sixths,  and 
sevenths. 


30 

Minor  2ds 


i 


¥ 


etc. 


:sz:: 


i 


V 


■K 


P=^' 


etc. 


31 

Minor  3ds 


r^ 

1 

~tk — H — 

— 1 — 

LP=^g— ^ 

Z 

etc. 


i 


tr-^^^r 


m 


,i2S: 


t?'^^ 


etc. 


m 


^jetc. 


32 

Minor  6ths 


!^ 


etc. 


-6^ 

33 

Minor  yths 


i?S: 


ri 


-t75^ 


1"^-^ 


P 


f^-^ 


i 


t 


:&<^ 


^.-^i: — \f^ 


I'^'ffi 


if^ 


etc. 


etc. 


The  distance  of  a  diminished  interval  is  a  chromatic  half  step  less 
than  that  of  the  perfect  or  minor. 

Write,  successively,  diminished  thirds,  fourths,  fifths,  sixths,  and 
sevenths. 


lO 


CUMULATIVE    HARMONY 


34 

Diminished  3ds 


sil' 


--W^\ 


?il=h 


f^m^ 


etc. 


Intervals  on  notes  marked  *  are  not  expressible  in  notation  and 
are  not  used  in  harmonic  combinations. 

35 

Diminished  4ths 


ife^K^is 


riSSiu-ii  etc.  =: 


^^•^irFS^^ 


l22iiJ 


36 

Diminished  Sths 


1*-* 


^ 


37 

Diminished  6ths 


f^^^ 


^zJetc. 


etc. 


^^35^i^g|"-^J 


il2z: 


Si 


38 

Diminished  7ths 


:|g=5^g^=2=tf^^^| 


etc. 


^J=^ 


I _| *  I  I I 


i=^^^^ 


f^«^ 


The  distance  of  an  augmented  interval  is  a  chromatic  half  step 
greater  than  a  perfect  or  major. 

Form  and  write  augmented  primes,  seconds,  thirds,  fourths,  fifths, 
and  sixths. 

39 

Augmented  primes 


i 


im 


-TZ^^Z^ 


etc. 


i 


^i=p?^&5=^ 


etc. 


E^^ 


l-^-^-^ir-^H^ xc> 


etc. 


i 


40 

Augmented  2ds 


Wp^^ 


:x^ 


etc. 


rsr-^ 


i?2^ — «- 


^ 


S 


etc 


|.i      yJ     y       .(s!— 11| 


3^i 


INTERVALS 


II 


41 
Augfmented  jds 


:xg=zzt 


^1^'^-^^^ 


m 


■^m^ 


etc. 


i 


p=^p^=^'(^- 


^^^- 


42 

Augmented  4ths 


43 

Augmented  sths 


etc 


i 


-&S?- 


44 

Augmented  6ths 


--^-^ 


etc. 


i 


c^ 


i 


p 


S3:" 


i^^F 


:^ 


etc 


-i?^ 


^t^= 


Si 


etc. 


x^=z:Ji«t 


l^ztt^it^i^t^ 


*i=:i|5=^! 


etc. 


The  student  should  be  required  to  become  thoroughly  familiar  with 
the  number  of  steps  and  half  steps  contained  in  the  various  intervals. 

Oral  practice,  such  as  follows,  is  invaluable: 

What  note  is  a  third  from  C?  from  E?  from  G,  etc. 

What  note  is  a  sixth  from  D?  etc. 

What  general  interval  does  E-C  form? 

How  many  steps  and  half  steps  are  contained  in  a  major  third?  a 
perfect  fifth?  a  minor  sixth,  etc. 

What  specific  interval  does  C-A  form?  Eb-A?  D^f-A?  etc. 

It  is  a  matter  of  the  utmost  importance  to  the  student  that  he 
should  take  a  thorough  course  in  musical  dictation  or  ear  training  in 
conjunction  with  these  studies,  in  order  to  attain  the  power  of  readily 


12 


CUMULATIVE    HARMONY 


distinguishing  tone  intervals  upon  hearing  them  sounded  together  or 
in  succession.  Too  much  consideration  cannot  be  given  to  this 
recommendation. 

In  the  formation  of  an  interval,  care  should  be  taken  to  determine 
the  number  of  staff  degrees  involved,  to  conform  to  its  general  name, 
and  then  to  arrange  the  interval,  by  proper  use  of  accidentals,  in  such 
manner  that  it  will  contain  the  required  number  of  steps  and  half 
steps. 

/IF, 

(a)  (d)  (c)  id) 


45 


* 


Td 


£E^: 


:i2^ 


At  (a)  the  number  of  staff  degrees  involved  is  two  [C  and  D],  form- 
ing a  general  interval  of  a  second.  As  the  distance  in  steps  and  half 
steps  is  i}4,  the  specific  name  is  an  augmented  second.  At  (b), 
while  the  number  of  steps  and  half  steps  is  i  ^  as  at  (a),  the  number  of 
staff  degrees  involved  is  three  [C,  D,  and  E],  resulting  in  a  specific 
interval  of  a  minor  third.  In  like  manner  the  number  of  steps  and 
half  steps  at  (c)  and  (d)  is  the  same;  the  number  of  staff  degrees 
involved  shows  them  to  be  respectively  a  diminished  fifth  and  an 
augmented  fourth. 

The  inversion  of  an  interval  is  effected  by  raising  the  lower  note 
an  octave. 

46 

By  inversion: 

A  prime  becomes  an  octave. 
A  second  becomes  a  seventh. 
A  third  becomes  a  sixth. 
A  fourth  becomes  a  fifth. 
A  fifth  becomes  a  fourth. 
A  sixth  becomes  a  third. 
A  seventh  becomes  a  second. 
An  octave  becomes  a  prime. 

Prime         octave  2d  7  th  3d  6th  4th  5th 


47 


g 


# 


'*f   r     f 


r 


— g^- 


5th 


4th 


INTERVALS 

6th  3d  7  th 


13 


2d 


pnme 


i 


I 


::^: 


w- 


f 


I 


r 


r 


Also  by  inversion : 


48 

Perfect 


g 


A  perfect  interval  becomes  a  perfect. 

A  major  interval  becomes  a  minor. 

A  minor  interval  becomes  a  major. 

An  augmented  interval  becomes  a  diminished, 

A  diminished  interval  becomes  an  augmented. 

perfect     per.         per.        major   minor     major     minor      minor    major 


d: 


:i2^=fe^: 


:i 


-75*- 


C         -i5»- 


^ 


-■U=P^ 


:i?^ 


r-T 


i 


major      aug. 

I 


dim. 

J- 


aug.      dim.        dim.      aug.        dim.       aug. 


ii 


U- 


S 


-^ 


iS 


^=fe 


■^ 


f 


Therefore  by  inversion: 

A  perfect  fifth  becomes  a  perfect  fourth. 

A  major  sixth  becomes  a  minor  third. 

A  minor  second  becomes  a  major  seventh. 

An  augmented  prime  becomes  a  diminished  octave. 

A  diminished  seventh  becomes  an  augmented  second. 


49 


;i>22: 


^(5* 9-^19 


'^^ 


s 


:J: 


^ ^ 


— #^5<2- 


:p: 


I 


=^22: 


Intervals  are  consonant  or  dissonant. 

A  consonance  is  an  interval,  which,  from  its  nature  and  quality, 
does  not  suggest  or  require  a  further  progression  or  resolution;  it 
may  be  classed  as  an  interval  of  repose. 


50 


m 


■^ 


^^ 


etc. 


14 


CUMULATIVE   HARMONY 


By  playing  these  intervals  separately  (as  they  have  no  connection 
with  each  other)  the  student  will  readily  recognize  the  effect  of  re- 
pose; that  is  to  say,  they  do  not  seem  to  demand  a  progression  or 
resolution  to  an  interval  of  different  nature  and  quality  in  order  that 
a  sense  of  completeness  may  be  reached,  as  is  the  case  with  the  inter- 
vals in  the  following  example  of  dissonances: 


51 


^ 


-mr- 


^ 


m 


By  playing  these  intervals  (the  unbracketed  ones)  the  student  will 
at  once  recognize  a  feeling  of  incompleteness  and  lack  of  repose,  a 
demand  for  a  succeeding  interval  of  different  quahty  (as  bracketed), 
in  order  that  a  sense  of  repose  and  completeness  may  be  realized. 
Therefore, 

A  dissonance  is  an  interval,  which,  from  its  nature  and  quality, 
suggests  or  requires  a  further  progression  or  resolution,  and  may  be 
classed  as  an  interval  of  motion. 

The  consonances  are  the  perfect  intervals,  and  the  major  and  minor 
thirds  and  sixths. 


52 


i 


-z^ 


ibg: 


^ir 


The  dissonances  are  the  major  and  minor  seconds  and  sevenths, 
and  all  augmented  and  diminished  intervals,  as  in  the  following  table: 


53 


aug. 

prime 


mm. 
2d 


maj. 
2d 


aug. 
2d 


dim. 
3d 


aug. 
3d 


dim. 
4th 


w' 


i2ik- 


^ 


"?ti^ 


tT-(&- 


i^ 


i 


aug. 
4th 

1 


dim. 
5th 


aug. 
5th 

m 


dim. 
6th 


aug. 
6th 

— r 


dim. 
7  th 


mm. 
7  th 


maj. 
7  th 


dim. 
octave 


-^^r^^-^ 


INTERVALS 


IS 


While  this  classification  is  clearly  represented  by  the  notation, 
certain  consonances  and  dissonances  which  are  enharmonically 
similar  may  be  identified  by  the  hearer  only  through  progression  to 
a  succeeding  interval. 


54 


i 


iy=ij=ii 


'^^^ 


H  vi    '^ii—^. 


The  perfect  fourth  was  formerly  considered  a  forbidden  dissonance, 
and  while  it  is  now  classed  as  a  consonance,  it  possesses  a  strong 
element  suggesting  further  progression. 

Play  these  exercises,  and  have  them  played. 


CHAPTER   III 
CHORDS 

A  chord  is  a  combination  of  three  or  more  tones  built  in  a  series 
of  thirds  upon  a  given  tone  called  a  fundamental  (or  root)  as  repre- 
sented by  corresponding  notes  on  the  staff. 

A  triad  is  a  combined  third  and  fifth. 


55 


3d         5tb 


{a) 
triad 


(^)       (O 


I 


At  (a)  the  combined  third  and  fifth  form  the  triad  of  C;  at  {h)  the 
triad  of  E;   and  at  (c)  the  triad  of  B. 
A  major  triad  consists  of  a  (combined)  major  third  and  perfect  fifth. 


At  {a)  a  combination  of  the  major  third  D-Ftr  and  a  perfect  fifth 
D-A  forms  the  major  triad  of  D;  at  {b)  the  major  triad  of  Eb;  at  (c) 
the  major  triad  of  B;  at  {d)  the  major  triad  of  Gb. 

Combine  and  write  major  triads  on  each  degree  of  the  scale  of  C, 
also  its  elevation  and  its  depression. 


etc 


A  minor  triad  consists  of  a  minor  third  and  perfect  fifth. 

i6 


CHORDS 


17 


58 


nun.         per.     minor 
(a)   3d  sth      triad  .  (i>)        (c)        {d) 


pg^ 


^¥^ 


m 


=::it 


^ 


At  (a)  the  combination  of  a  minor  third,  C-Eb,  and  a  perfect  fifth, 
C-G,  forms  a  minor  triad  on  C;  at  {h)  the  minor  triad  on  E;  at 
{c)  the  minor  triad  on  A;  and  at  {d)  the  minor  triad  on  Bb. 

A 

Form  and  write  minor  triads  on  each  degree  of  the  scale  of  C,  also 
on  its  elevation  and  its  depression. 


etc. 


^^S^ 


etc. 


An  augmented  triad  consists  of  a  major  third  and  an  augmented 
fifth. 


60 

maj.     aug.     aug. 

(a)   3d       5th     triad     {b)        {c)         (d) 


^^m^^^ 


At  (a)  the  major  third,  C-E,  and  augmented  fifth,  C-G#,  com- 
bined, form  the  augmented  triad  on  C;  at  (b)  the  augmented  triad 
on  E;  and  at  (c)  and  (d)  the  augmented  triads  on  Al?  and  Bb  re- 
spectively. 

A 

Form  and  write  augmented  triads  on  each  note  of  the  scale  of  C, 
also  on  its  elevation  and  its  depression. 


61 


etc. 


^^^^"- 


The  augmented  triad  on  B^  cannot  be  expressed,  and  is  not  used  in 
harmonic  combination. 
A  diminished  triad  consists  of  a  minor  third  and  diminished  fifth. 


i8 


CUMULATIVE   HARMONY 


62     min.      dim.     dim. 
(fl)  3d        5th      triad 


(^).      (O         {d) 


y— ^^-b^i: 


^ 


At  {a)  the  minor  third,  C-Eb,  and  the  diminished  fifth,  C-Gb,  form 
the  diminished  triad  on  C;  at  (6),  (c),  and  {d)  are  examples  of  dimin- 
ished triads  on  E,  F#,  and  A#  respectively. 

Form  and  write  diminished  triads  on  each  degree  of  the  scale  of 

A 

C,  also  on  its  elevation  and  its  depression. 


etc. 


^0^^  ^''''  ^^l^^^^fcU 


etc. 


CHAPTER   IV 


HARMONIZATION   IN  FOUR  VOICES  OVER  A   GIVEN  BASS 

As  a  triad  contains  but  three  notes,  one  of  them  must  be  dupli- 
cated in  four-part  writing.  This  is  called  doubling.  The  funda- 
mental is  considered  the  most  suitable  for  doubling,  the  fifth  may  be 
freely  doubled,  but  for  the  present  the  student  should  avoid  doubling 
the  third. 


64 


(«) 


ib)  ic) 


m 


-ish 


--^ 


id) 


At  {a)  the  fundamental,  C,  is  doubled;  that  is  to  say,  it  occurs  in 
two  different  voice  parts. 

At  {h)  the  fifth,  G,  is  doubled;  at  (c)  the  fundamental,  F,  is  doubled; 
while  at  {d)  the  doubled  note  is  the  fifth,  A. 

In  four-part  writing  the  voices  are  known  by  the  names  given  them 
in  vocal  music;  from  highest  to  lowest  they  are  called,  respectively, 
soprano,  alto,  tenor,  and  bass. 

Soprano  Alto  Tenor  Bass 


65 


^=± 


3 


^i 


-f2 ^- 


-^ — s^ 


-iS"- 


3 


s^— ^ 


Progression  of  Voices 

Wlien  a  voice  moves  from  one  note  to  another  a  scale  degree  above 
or  below,  it  is  said  to  progress  by  degree  (or  diatonically) ;  when  it 
moves  more  than  one  scale  degree,  it  is  said  to  progress  hy  skip; 
when  it  moves  in  a  succession  of  half  steps  by  means  of  chromatically 
altered  notes,  it  is  said  to  progress  chromatically. 

19 


20 


CUMULATIVE   HARMONY 


66 


f 


tiifc 


^ 


In  this  example  each  note  proceeds  to  the  next  scale  degree  above 
or  below,  therefore  progressing  by  degree  (or  diatonically). 


67 

f) 

/                                              1 

1 

1            1 

i 

\           1             !             1           J 

1 

1             1             ,           J 

\j^    -^ 

* — 

— #— 

— - — ' 

I — ,5^_ 1 

• 

—^ 

1     -      " 

1 — ^ 1- 

Here,  on  the  contrary,  each  note  proceeds  to  another  at  a  distance 
of  a  third  or  more,  thus  progressing  by  skip. 


68 


i 


i 


^ 


:i?k: 


t 


-'^K 


^P 


±: 


In  this  example  most  of  the  notes  proceed  a  half  step,  by  means 
of  chromatic  alterations,  to  the  next,  producing  chromatic  progres- 
sions. 

Two  voices  moving  in  the  same  direction  are  said  to  progress  in 
similar  motion. 

69 


i 


«- 


I 


-^ 


When  they  move  in  opposite  directions  they  are  said  to  progress 
in  contrary  motion. 

70 


^^ 


-&- 


-a- 


When  one  voice  remains  stationary  and  the  other  ascends  or  de- 
scends, they  are  said  to  progress  in  obliqtie  motion. 


71 

n 

1 

1 

1 

I 

y                  -si 

'             ; 

1 

\ 

^          ej.           '-^ 

-^ 

r^ 

Ci          1 

-H                   *1 

^            1 

\(\ 

^' 

^\ 

; 

fD          \ 

^                     1 

^            1 

\v  t       ^           ^ 

(5/ 

1 

%J 

eJ 

SJ 

o          ■- 

^  Notes  common  to  two  chords  to  be  connected  should  be  retained 
in  the  same  voice,  the  other  voices  proceeding  to  the  nearest  available 
positions. 


HARMONIZATION    IN    FOUR  VOICES 


21 


This  is  particularly  applicable  to  the  inner  voices  —  the  alto  and 
the  tenor;  the  soprano  frequently  requires  considerable  freedom  of 
movement  in  order  to  obtain  good  melodic  results;  the  bass  often 
moves  in  succession  of  skips  to  good  effect.  Similar  motion  in  all 
four  voices  should  be  avoided,  care  being  exercised  toward  effecting 
contrary  motion,  or  a  common  tone  sustained  in  the  same  voice. 


72 


(^) 


A  J?    4       J  J 

e> 

V^ — ^=1 

\ — ^' n 

< 

(^•-—^ r— 

\^\ 

—<S. Is^ 

1 

— fSi 

—  -'9- 

^ 

[^ 5'— 

tIZI ^ 1 

«> 

^ 

At  (a)  the  note  common  to  the  first  and  second,  and  the  second 
and  third  as  well,  is  G,  which  occurs  in  the  alto  in  the  first  voice,  and 
should  be  retained  in  the  alto  in  the  second  and  third  chords.  At 
(6)  the  note  common  is  C,  which  is  retained  in  the  tenor. 


73 


ii 


m 


■^ 


-^ 


W^^ 


^^^t. 


ji— fe^ 


[m 


^ 


3^ 


Transposition  is  a  change  of  key  by  means  of  a  corresponding 
change  of  notation  and  signature  or  the  sounding  of  tones  represented. 

A 

Exercise  73,  transposed  to  Eb,  appears  as  follows: 


74 

1      J 

< 

-a- 
a 

=^ 

etc. 

=^=T- 

T — h 

^ 

\^H        1             ' 

^      1 

—^- 

\ — 

C*        1 

fil- 

Taking  the  model  (Exercise  73)  as  a  pattern,  the  student  should 
form  triads  on  the  following  bass  sets,  in  accordance  with  the  instruc- 
tions given  above. 


22 


CUMULATIVE   HARMONY 


75 


:19: 


t — #- 


I 


-«''-=- 


76 


^ 


S: 


77 


— =t — 1 — ^ai # — ' — ' 

i-^ «i LT , 

0 1 

■g^ [-? 


I 


^ 


The  student  may  use  the  ist,  3d,  or  5th  for  the  initial  note  in  the 
soprano;   this  presents  three  modes  of  working  out  each  exercise. 

Transpose  these  examples  as  in  Exercise  74  to  several  keys,  and 
work  out  as  before. 

The  difference  of  altitude  in  the  various  voice  parts  does  not  affect 
their  interval  relation  with  the  bass. 

Hence  all  the  following  are  major  triads  of  C,  with  the  funda- 
mental as  the  actual  bass. 


78 

<3 

-tg- 

1    V 

6> 

/r 

S> 

m 

— 19 — 

— -s — 

G> — 

<9 

{ 

^ 

-&- 

— s> — 

-G>- 

— (9 — 

-<5>- 

-«5>- 

i  (m\'        ^^ 

r^ 

s? 

\pj'       c> 

25 

\1^       &> 

f^ 

_    e> 

\                                                                                                        II 

The  usual  compass  of  the  various  voices  in  vocal  music  is  given  in 
the  following  model,  the  open  notes  indicating  the  preferred  compass, 
the  filled  notes  including  a  possible  extension. 


HARMONIZATION    IN    FOUR   VOICES 

79 
Soprano 


23 


Alto 


Tenor 


Bass  ^ 


m 


^M: 


^^ 


-i9- 


i 


:(^): 


P^ 


C^)-^- 


l^i^)^ 


U-) 


7i7 


It  is  desired  that  the  four  voices  be  kept  as  nearly  equidistant  as 
possible,  the  upper  three  voices,  as  a  rule,  occurring  within  an  octave 
of  each  other.  The  soprano  and  alto  at  times  may  exceed  this  distance, 
while  the  bass  part  is  frequently  written  without  regard  to  its  distance 
from  the  tenor.  These  exercises  should  be  worked  out  in  both  close 
and  open  position. 

Play  these  exercises,  and  have  them  played. 


CHAPTER  V 

INVERSION  OF  TRIADS 

By  inversion  of  a  chord  is  meant  the  placing  of  one  of  its  notes, 
other  than  the  fundamental,  in  the  bass. 

When  the  fundamental  of  the  chord  is  used  as  the  bass,  the  chord 
is  in  fundamental  position. 

80 


:^ 


m 


:i 


-1^ 


In  the  above  model  the  triads  of  C,  F,  and  G  are  given  with  the 
fundamentals  C,  F,  and  G  in  the  bass  part,  and  are  therefore  in  funda- 
mental position. 

In  the  inversions,  avoid  doubling  the  bass  except  in  the  chord  of  f . 

When  the  third  is  used  as  the  bass,  it  is  in  the  first  inversion. 

81 


-A 


^ 


■^- 


m 


4- 


=S 


d= 


-z^ 


In  this  example  the  same  chords  are  given,  with  the  thirds  E,  A, 
and  B  in  the  bass;   they  are,  therefore,  in  the  first  inversion. 

When  the  fifth  is  in  the  bass,  the  chord  is  in  the  second  inversion. 


82 


-g- 


-2^ 


-<S>- 


24 


INVERSION    OF   TRIADS 


25 


The  same  chords,  with  the  fifth  from  the  fundamental  in  the  bass, 
are  in  the  second  inversion. 

Figured  bass  is  the  employment  of  figures  placed  above  or  below 
the  bass  notes,  to  indicate  the  intervals  represented  in  the  various 
chords.  Intervals  are  computed  upward  from  the  lowest  note  (the 
bass). 


83 


1/                                   1 

/  /T 

<5 

<^ 

rj 

fp 

<3 

If 

■i 

V 

} 

g 

& 

g 

g 

< 

8 
5 
3 

5 
3 

5 

3 

i^.                                                                          1 

r 

i: 

1 

/51 

rj 

<<> 

^ 

0                \ 

\                                1 

We  have  here  given  an  example  of  figuring  the  triad  of  C,  which, 
complete,  is  |.  For  the  sake  of  abbreviation,  the  figure  8  is  rarely 
used;  3,  5,  or  both,  are  used  only  when  the  particular  interval  repre- 
sented is  to  be  affected  by  an  accidental  sharp,  flat,  or  natural;  also, 
for  abbreviation,  the  figure  3,  when  affected  by  an  accidental,  is 
omitted,  the  sharp,  flat,  or  natural  alone  representing  the  third  so 
altered;  thus: 


84 


{a) 


(*) 


(c) 


=^ 


6f 


b5 


f' 


At  (a)  the  b  alone  indicates  the  triad  with  the  third  flat  —  C,  Eb, 
G.  At  (b)  the  b5  represents  the  triad  with  the  fifth  flat  —  Eb,  G, 
Bb;  and  at  (c)  the  i^  and  #5  represent  the  triad  with  the  third  and 
fifth  sharp  —  B,  D^,  and  F#. 

In  the  first  inversion  of  the  triad  the  third  from  the  fundamental  is 
assigned  to  the  bass,  forming  the  intervals  of  a  third  (3d)  and  sixth 
(Cth)  from  that  note.    Figured,  |  or  6. 


26 


CUMULATIVE    HARMONY 


85 

{b) 

(O 

{d) 

/  y                         ' 

I  A       rs 

fj 

'^ 

1 

,^^ 

\^ % 

'9 

— <5 

— t 

^ 

y              3 

-'9- 

6 

6 

b 

6 

U?^ ^^ 1 

— b^^ 

r^ 

— w . 

1^. ^ 

—  r 

-^ 

\                                        1 

At  (a)  is  given  the  first  inversion  of  the  triad  of  C,  with  the  third, 
E,  in  the  bass;  the  intervals  appearing  from  the  bass  note  are  as 
follows:   E  to  G  a  3d,  E  to  C  a  6th. 

The  figures  f  are  abbreviated  to  6.  At  (6)  is  given  the  first  in- 
version of  the  minor  triad  of  C,  with  Eb  as  the  actual  bass. 

At  (c)  is  given  the  first  inversion  of  the  major  triad  of  Eb,  with  G 
in  the  bass,  and  with  the  third  flat  and  sixth  flat  (as  the  figure  3, 
when  chromatically  altered,  is  represented  by  the  chromatic  alter- 
ation alone,  in  this  case  the  b  represents  b3);  and  at  id)  occurs  the 
first  inversion  of  the  major  triad  of  B,  with  Ti^  in  the  bass,  B  being 
the  sixth  and  F#  the  third  from  the  bass. 

In  the  second  inversion  of  the  triad,  the  5th  from  the  fundamental 
is  assigned  to  the  bass;  the  intervals  thus  formed  from  this  bass 
being  the  6th  and  the  4th.     Figured,  f . 


86 


{a) 


W 


{c) 


id) 


b6 
4 


^^ 


6 

J2i2_ 


4i 


At  {a)  is  given  the  second  inversion  of  the  major  triad  of  C,  with 
G,  the  5th  from  the  fundamental,  in  the  bass,  forming  the  intervals 
of  a  6th,  E,  and  a  4th,  C.  At  (h)  the  inversion  of  the  triad  of  C 
minor  is  the  same  in  all  respects  as  at  (a),  except  that  the  sixth  is 
Eb;  at  (c)  the  major  triad  of  Eb  appears  in  its  second  inversion,  with 
Bb  in  the  bass;  and  at  {d)  is  the  second  inversion  of  the  major  triad  of 
B,  with  F#  in  the  bass. 

In  the  following  exercises,  the  student  will  add  the  proper  notes 
of  harmony  in  the  soprano,  alto,  and  tenor,  as  indicated  by  the  figured 


INVERSION    OF   TRIADS 


27 


bass,  and  with  the  various  voice  parts  progressing  according  to  the 
directions  given  above.  An  example  of  this  mode  of  procedure  is 
given  in  the  following  model. 


87 


(a)         {l>)  (c) 


id) 


^^ 


m 


^ 


^ 


^^^-•^ 


-K^ 


-^^^ 


12^ 


(i! 


z^r- 


^7^ «M 


-riri 


-25*- 


In  cases,  as  at  (a),  where  the  doubled  note  is  the  one  common  to 
that  chord  and  the  succeeding  one  (6),  it  is  not  necessary  that  this 
note  should  be  retained  in  both  voices,  as  good  chord  connection 
may  be  obtained  through  one  common  note  being  retained. 

At  (c)  the  figuring  (6)  indicates  the  3d,  G,  and  the  6th,  C,  as  the 
notes  to  be  added  to  the  given  bass,  forming  the  first  inversion  of 
the  triad  of  C;  as  the  bass,  E,  is  not  to  be  doubled  in  this  inversion, 
the  available  notes  in  the  three  upper  voices  are  G  and  C,  and  of 
these  the  nearest  one  to  which  the  soprano  note,  A,  in  the  preced- 
ing chord,  may  progress  is  G.  This  is  likewise  the  nearest  point  for 
progression  of  the  alto  note,  F,  at  (6),  which  results  in  a  doubling  of 
the  G  on  the  same  degree  of  the  staff. 

As  the  most  satisfactory  progressions  are  in  contrary  motion  of  a 
part  or  all  of  the  upper  voices  with  the  bass,  the  C,  which  is  common 
to  the  chords  at  (a)  and  (6),  is  retained  in  the  tenor  rather  than  in 
the  soprano,  thus  causing  the  soprano  and  alto  to  move  contrary  to 
the  bass,  in  the  preferred  progressions. 

A  similar  case  is  at  (c),  where  the  G  of  the  soprano  moves  upward 
to  B,  in  contrary  motion  to  the  bass. 


28 


CUMULATIVE   HARMONY 


88 


Ege 


S 


-z^ 


e 


^3 


6      6 

4 


6         6 
4 


^^f-^ 


89 


-s< ^ 


-(S2_ 


■s*- 


00 


-75^- 


6         6         6 
4  4 


6        6 
4 


6        6 
4 


i 


-Z^feH 


^ 


^ 


?6^     ^  b-^z=g 


91 


b6        6 
4 


6        6  6 

4 


33 


S 


-sf- 


:2:^ 


-^M-^ 


gHhP'g^ 


92 


6       ^^6 
4 


"S^IJ^:^ <s^ 


6 
4 


^i 


e 


=5=^ 


93 


;S 


#6 
4 


6  5 

4 


S 


4: 


-?5^ 


6  #6  6 

4 

In  these  exercises  examples  of  chromatically  altered  notes  appear, 
both  in  the  bass  and  in  the  other  voices  as  indicated  in  the  figuring. 
Care  must  be  exercised,  in  transposing  to  other  keys,  toward  correct 
chromatic  indications  of  notes  that  are  marked  to  be  elevated  (chro- 
matically raised)  and  depressed  (chromatically  lowered). 

In  vocal  music  the  four  voices  are  generally  written  in  open  (or 
dispersed)  position,  with  a  note  place  of  the  initial  chord  vacated  be- 
tween the  soprano  and  alto  which  is  occupied  on  the  bass  staff  (an 
octave  lower)  by  the  tenor.  This  mode  of  writing  the  tenor  on  the 
lower  staff  with  the  bass  should  be  practiced  quite  as  frequently  as 
that  of  writing  the  three  upper  voices  on  the  upper  staff. 


INVERSION    OF   TRIADS 


29 


94 


i 


d 


i 


i 


=^7^ 


-f:^-rJ—r^=-g:)-—-T!:)^- 


T 


fg      1^ 


(^ 


:J^ 


2^: 


I     I 


=i 


<^  — C-^-Eg 


r"^^ 


■^2i!- 


'- ^-|g- 


It  will  be  seen  that  the  notes  assigned  to  the  alto  in  Exercise  87 
are  given  to  the  tenor  in  Exercise  94,  by  being  lowered  an  octave. 


05 


(PSS 


-«s^«*-=  --g 


(g 


^ 


g 


I 


3Z 


•^ 


b6 


When  a  combination  of  notes  forming  a  chord  is  arranged  in  such 
manner  as  to  appear  in  a  series  of  thirds,  the  lowest  note  (when  the 
chord  is  complete)  is  the  fundamental. 


06 


i 


(«) 


(A) 


(O 


{d) 


^^- 


{e) 


-^L 


^% 


£=t 


'^^ 


i 


?=r 


^ 


lii 


At  (a)  the  chord  E,  G,  C,  when  rearranged  to  appear  in  a  series  of 
thirds,  is  seen  to  have  C  for  its  fundamental;  at  (6)  G  appears  as  the 
fundamental;  at  fc),  Db;  and  at  (</),  B.  At  {e)  the  bass  note,  A,  is 
the  fundamental  as  it  stands. 


30 


CUMULATIVE    HARMONY 


The  following  examples  should  be  worked  out  as  above,  in  both 
close  and  open  positions,  and  transposed  to  other  keys  for  similar 
treatment. 

97 


^ — ^ 


-r^ 


sy- 


# m^ 


6  6 

4 


b6 


6  6 

4 


m 


:"M|^ 


:**: 


i^6 


-'9-^ 


1 


^6 
4 


98 


:.  /  >  ■?- 


=^^==J= 


5 


6         6 
4 


'®^^^~ 

(22— 

a 

— ^ — 

F^=^ 

i — [ri— 

J      J   \r. 

«> 

1 

1 

-- i?^ d — ^ 

— V 

9            ^ 

6         6 
4 


t|6         6 
4 


m 


i=if^ 


»  ^ 


^ 


6       6 
4 


99 


hm 


^ 


i^mt 


:i?^ 


3=ft 


6      6 
4 


#6 
4 


m 


^ 


:|* 


S5 


m. 


^ 


g 


S6 
4 


-0-^ 


-J-^i-^TTl~ 


I 


-iS>-r- 


6       6 
4 


Exercise  95  may  be  utilized  in  the  same  manner. 
Play  these  exercises  and  have  them  played. 


CHAPTER  VI 

THE  CONSTRUCTION  OF   MELODIES  OVER 
ACCOMPANIMENTS 

In  constructing  melodies  from  a  prepared  accompaniment  such  as 
may  be  formed  from  the  worked-out  Exercise  94,  the  student  is  at 
liberty  to  use  the  notes  contained  in  the  upper  three  voices  as  freely 
as  desired,  and  at  any  altitude.  Any  of  these  three  notes  may  be 
duplicated  at  will,  as  it  is  not  to  be  considered  faulty  doubling;  but 
it  must  be  remembered  that  such  doubling  as  is  disallowed  between 
the  bass  and  any  of  the  upper  voices  is  also  forbidden  between  the 
bass  and  the  melody. 

The  student  should  make  a  table  of  rhythmic  figures  in  conmiOn 
(I)  time,  using  half,  quarter,  dotted  quarter,  eighth,  and  combined 
dotted  eighth  and  sixteenth  notes,  from  which  he  can  draw  for  use  in 
the  construction  of  melodies. 

It  is  desirable,  at  present,  that  the  melodies  should  be  of  broad 
song  style,  and  as  tuneful  as  possible. 

At  the  fourth,  eighth,  and  sixteenth  bars,  greater  length  of  notes 
may  be  used,  forming  points  of  repose,  in  order  to  conform  to  certain 
practices  of  musical  form. 

Exercise  94  will  now  be  used  as  an  accompaniment  upon  which  an 
example  of  melody  is  to  be  constructed. 


100 


{a) 


ib) 


i 


ic) 


{d) 


^^ 


d=t 


(i 


^ 


1 


31 


-A 


i^ 


-751 — -"s= 


32 


CUMULATIVE   HARMONY 


It  may  be  noticed  at  (a)-(6)  care  has  been  taken  to  avoid  using  the 
E  of  the  bass  in  the  attending  melody,  as  it  would  be  a  faulty  doubling 
with  the  three  upper  voices,  and  consequently  not  allowed  in  the 
melody  during  the  Hfe  of  that  chord.  At  (c)-(d)-(e)-{f),  etc.,  the 
third  is  freely  dupUcated  without  the  effect  of  faulty  doubling  of 
the  third  from  the  fundamental. 

The  soprano,  alto,  and  tenor  should  be  placed  at  an  altitude  quite 
near  the  bass,  in  order  that  a  more  sonorous  sound  body  may  be 
obtained  for  the  accompaniment,  and  a  clearer  field  for  occupation 
by  the  melody.  At  (a)  in  the  following  exercise  the  D^  ascends 
to  the  T^,  in  order  to  provide  four  different  notes  for  various  forms 
of  accompaniment. 

At  the  fourth,  eighth,  twelfth,  and  sixteenth  measures,  the  melody 
rhythms  consist  of  notes  longer  than  the  prevailing  ones;  this  is  done 
in  order,  through  the  effect  of  rhythmic  repose  thus  obtained,  to  aid 
in  dividing  the  melody  into  phrases. 


101 


^ 


£ 


:!=: 


■1=2- 


(a) 


i 


m 


7b- 


-?b- 


^2- 


THE   CONSTRUCTION    OF   MELODIES 


33 


i 


:ifc^ 


B 


m 


£ 


£=^fx^i?^ 


^ 


w 


i 


3 


-s^ 1^- 


S-^5^ 


:e 


r 


=^- 


4; 


r 


^te 


r 


I 

4 


m 


5S 


i 


:^i^ 


-Bf- 


%J     .§- 


r.-i5*- 


r 


f 


t!i 


r 


i 


^ 


■^2- 


r 


b6 


i 


p^ 


5 


i 


i^ 


-25»- 


T" 


^ 


I    r 


r 


The  positions  of  the  various  voice  parts  may  be  changed  from  one 
note  of  a  chord  to  another,  provided  it  is  done  without  altering  the 
tonal  content  of  the  chord.  The  most  frequent  mode  of  accomplish- 
ing this  is  by  exchanging  notes  assigned  to  various  voices,  one  with 
another,  during  the  life  of  the  chord;  this  may  afifect  one,  two,  or 
three  notes,  or  the  entire  chord. 


34 


CUMULATIVE   HARMONY 


102 


i 


^ 


J^M 


W 


f=f 


r-r-r 


-i 


3t 


J 


K!; 


^ 


f^ 


r^ 


6    -    5 


An  additional  exercise  for  similar  treatment  follows. 

103 

J  <  <->.■  I  I  J.J  J ^  J..I 


i^^ 


(i 


J- 


etc. 

I 


ii 


=*^ 


s 


^ 


-^--(2. 


-'S-Tg^ 


gj      ^\(^ 


4    # 


:5*- 


6      6 
4 


-^^ 


6       6 
4 


Accompaniments 


We  will  now  pass  on  to  the  consideration  of  accompaniments  in 
various  forms  —  prepared  for  piano  performance  by  amplification 
of  exercises  in  four-part  writing. 

Accompaniments  are  formed  in  a  diversity  of  ways,  such  as  the  use 
of  the  various  notes  of  a  chord  in  repetition,  in  alternation,  as  after- 
beats,  by  the  formation  of  melodic  figures  from  arpeggios,  and  even  in 
imitation  and  other  contrapuntal  forms. 

A  number  of  examples  of  the  more  common  accompaniment  figures 
are  here  given. 

104 


y^y  i^  i.  i^  ^ 


*  *4  * 


#  >  > 


T 


1e==)c 


THE  CONSTRUCTION   OF   MELODIES 


35 


(tfjJ^J  »' J^^ 


a  u  -a 


W^ 


p^ 


^^ 


^ 


It  will  be  seen  that  the  harmonic  content  in  each  of  these  amplified 
examples  is  the  same  as  that  in  the  first  measure  of  Exercise  95,  with 
the  imderstanding  that  each  note  of  the  chord  (which  may  occur  in 
repetition)  represents  a  half-note  duration,  as  in  the  former  exercise. 
It  is,  in  fact,  harmonic  accompaniment  expressed  in  arpeggio  figures 
or  broken  chords.  By  amplifying  the  accompaniment  as  submitted 
in  the  second  figure  of  Exercise  104,  the  melody  and  accompaniment 
in  Exercise  95  would  appear  as  foUows; 


36 


CUMULATIVE   HARMONY 


105 


i 


^ 


T^- 


H=2- 


3 


(i^ 


etc. 


— \ \ 1 h 


11^ 

-0- ^^ ^ 


i 


-^H— ^ 


(i 


^^^ 


^c^ 


^ 


^ 


^^ 


:N=tc 


This  should  also  be  prepared  for  performance  of  the  combined 
melody  and  accompaniment  as  a  piano  solo,  with  the  four  voices  of 
the  harmony  on  the  bass  staff. 

106 


-(2- 


(a) 


4 


etc. 


i 


107 


i 


-h2^ 


W- 


1^ 


^ 


r_  ^    etc. 


m 


-g- 


-4i- 


>-:=^ 


^ 


1 


I  6  6 

4 

The  harmonic  content  of  the  accompaniment  at  (c)  is  illustrated  by  the  same 
chords  at  (b),  as  they  appear  before  being  amplified. 

The  above  given  basses,  as  well  as  those  that  follow,  should  be 
transposed  to  various  keys,  harmonized  in  various  accompaniment 
forms,  and  new  melodies  constructed  upon  them  in  accordance  with 
the  given  directions. 


THE   CONSTRUCTION   OF   MELODIES 


37 


When  preparing  them  for  piano  solo  performance,  the  three  upper 
voices  should  generally  be  kept  quite  within  the  following  compass. 


108 


fcr 


& 


m 


-g>- 


:l 


■i 


etc. 


n — \^ 


ht: 


i?r=^ 


^ 


f — r 


r 


Two  illustrations  of  melody  formation  from  a  harmonic  structure 
are  submitted 


m.  No.  3 


Macbeth,  "  Gavotte  for  Strings  " 


m 


j-a 


^ 


■t=^r^ 


S 


^ 


:^3tL 


i. 


^i?BE£ 


g-^-^ 


? 


4 


-*- 


^ 


-*-^ 


^— x-x- 


^e 


I 


■iSk- 


is: 


i: 


I  I 

•  The  C  is  a  passing  note  which  will  be  considered  later. 


lU.  No.  4  • 

>.^_ ^^ 


Schubert,  "  Wohin  ? " 


7^^=^^ 


i?a: 


^  •'^ 


-^ <^     M     •!        I     gl # 


i 


^ 


^ 


-\  o^-^  ^ 


38 


CUMULATIVE   HARMONY 


^ 


etc. 


tr 


1    S  .J.    0 ^        '     ^     J    ^     "^     0 


^^ 


i^ 


^;:^ 


— r r T r 

The  pedal  note  (a)  will  be  discussed  later;  the  bass  represented  is  D. 

A 

An  application  of  Exercise  95  transposed  to  Ab  is  here  given. 


109 

m^i    I       J    I   J       ^tq:-J       J=F= 


etc 


110 


i 


as 


^^ 


4: 


eta 


(1 


^^ 


fefcl* 


W^ 


-s*- 


^ 


^ 


£ 


(^ 


fel=^ 


etc. 


p 


sfcs= 


S 


Also  other  examples  for  similar  treatment. 


THE   CONSTRUCTION    OF  MELODIES 


39 


U2 


I       I        '         J      I  -79— fg       I   ^    =F 

H-^gi — 'g- — f° — i 


i 


g 


:2± 


6         6 
4 


6         5        6        6 
4  4 


113 


Ml 


^^ 


-:rT  ' !    fg' 


-9—1-^ 


fe^ 


i^ 


6       6 
4 


6         6        6 
4 


114 


^ 


^ 


■^2 «>- 


6    ,    6 
4 


6        6 
4 


il6        6 
4 


6       6 

4 


m_ 


o     ^  V^ 


E 


E 


-«&-tt5H 


--g f^'- 


-(5* G>- 


-7^ <»- 


t==f 


6     #6 
4 


S6         6 
4 


6        6 
4 


115 


im.]  jiJ  J|j^^^i# 


i 


^52- 


6        6 


6         5 
4 


6       6 

4 


6         5 

4 


m. 


i 


=?^ 


^ 


I 


tl^ 


??: 


:t=: 


«6 

4 


#6 
4 


6     #6 
4 


lie 


fi^ 


-?s< — ?:>- 


■K^ 


-t:> 


6      6      #  le      6      # 

4  4 


6         6 
4 


Pg^^ 


i 


I 


i 


^=?z 


•'S— s^- 


2z: 


6  6 

4 


6       6 

4 


6         5 
4 


Play  all  these  exercises  and  examples,  and  have  them  played. 


CHAPTER   VII 
PARALLEL   FIFTHS  AND   OCTAVES 

In  the  examples  for  chord  connection  given  thus  far,  one  or  more 
notes  are  common  in  each  two  chords  to  be  connected.  In  such  cir- 
cumstances good  binding  of  contiguous  chords  is  easily  obtained,  the 
notes  common  to  both  being  given  to  the  same  voice,  and  the  other 
voices  moving  naturally  from  their  positions  in  one  chord  to  positions 
lying  nearest  in  the  succeeding  one. 

In  cases  where  two  chords  to  be  connected  have  no  note  in  common 
the  various  voices  should  move  to  the  nearest  available  position  in 
the  next  chord,  in  such  manner  that  there  will  appear  no  faulty 
parallel  (consecutive)  5ths  or  8vs. 

Faulty  parallels  occur  when  two  voices  moving  in  similar  direction 
progress  chromatically  or  by  degree  in  perfect  5ths  or  8 vs. 

117 


bad 


bad 


bad 


not  bad 


not  bad 


E^^ 


Parallel  perfect  5ths  or  Svs  progressing  by  skip  are  generally  dis- 
agreeable in  the  outer  voices. 

118 


0 

1  y       — '^ 

iC-— ~ 

f   yf        ^ 

— , 

I  Ifh 

1^ 

\  \>\)     e? 

\ 

-        ^ 

(m\' 

^' 

a 

^"^ 

A  diminished  5th  followed  by  a  perfect  5th  is  objectionable  in  the 


outer  voices. 


119 


(g; 


40 


PARALLEL    FIFTHS    AND   OCTAVES 


41 


The  faulty  parallels  referred  to  above,  while  forbidden  by  the  laws 
of  harmony  and  generally  offensive  to  the  cultivated  ear,  are  often 
used  by  modern  composers  for  dramatic  and  other  effects,  the  justi- 
fication for  which  may  not  be  readily  understood  by  the  immature 
student;  he  is  therefore  cautioned  against  their  employment  in  any 
circumstances  until  his  work  is  sufficiently  mature  to  warrant  him  in 
assuming  an  authoritative  judgment  in  their  use. 


120 


(a) 


a>) 


(c) 


1^ 


^^ 


(^) 


^ 


■i  ^, 


f 


-sr 


(P 


Ezj^ 


-^ 


-«♦-. 


^= 


^^m 


W^ 


T5*- 


^ 


W^ 


-^ 


^ 


:si 


At  (a)  may  be  seen  parallel  8vs  between  the  soprano  and  tenor,  and 
parallel  5ths  between  the  alto  and  tenor. 

At  (6)  are  parallel  5ths  between  soprano  and  tenor,  and  8vs  be- 
tween tenor  and  bass.  At  (c)  are  parallel  8vs  between  alto  and  bass 
and  5ths  between  tenor  and  bass.  In  the  soprano  is,  also,  a  bad  pro- 
gression of  an  augmented  2d  from  F  to  G#,  which  should  be  avoided, 
particularly  in  the  outer  voices. 

At  [d)  there  are  parallel  Svs  between  soprano  and  bass,  and  5ths 
between  alto  and  bass. 


121 


The  same  bass  with  the  upper  three  voices  added  in  such  manner 
that  there  appear  no  faulty  parallels.  This  is  accomplished  by  caus- 
ing the  offending  voices  to  move  in  contrary  motion;  these  pro- 
gressions frequently  prevent  the  tones  common  to  two  chords  from 
being  placed  in  the  same  voice. 


42 


CUMULATIVE    HARMONY 


Additional  exercises  to  be  worked  out  as  above,  in  various  keys, 
follow. 


122 


gei 


i 


-(2- 


f^ 


#5 


123 


i 


2~~g^ 


-^^ 


r 


124 


gSfri^T 


f^ 


I 


-25»- 


:|^ 


-g>'    rg 


•zg~~r- 


It  is  suggested  to  the  instructor  that  the  foregoing  exercises  be 
thoroughly  worked  out  in  simple  harmonization  of  the  basses  in  the 
given  key,  transp>osed  to  many  other  keys  and  worked  out  similarly 
before  attempting  to  construct  melodies  thereon.  A  good  writing 
technique  in  chord  connection  is  an  absolute  necessity  through  all 
the  preliminary  stages  of  the  work. 

Play  all  these  exercises  and  examples,  and  have  them  played 


CHAPTER  VIII 


THE   DOMINANT  SEVENTH   CHORD 

Discords  are  chords  containing  dissonant  intervals. 

First  and  most  important  of  these  is  the  W  chord. 

This  chord  is  formed  by  adding  a  minor  yth  to  the  D  triad  (which 
should  always  be  major)  and  must  contain  the  intervals  of  a  major 
3d,  a  perfect  5th,  and  a  minor  yth;  figured  7.  This  is  applicable 
alike  to  major  and  minor  keys. 

126 

CFDA  ad  bf# 


^F^^m^^m^^^^^^^^^^^m 


The  D''  chord  is  of  peculiar  value  in  that  it  determines  absolutely 
the  key  or  tonality;  so  that,  regardless  of  the  initial  signature,  any 
combination  of  notes  that  consists  of  a  major  triad  and  minor  yth,  or 
an  inversion  of  the  same,  is  a  D^  chord,  the  fundamental  of  which  is 
the  Dominant  of  a  key  whose  Tonic  is  a  perfect  5  th  below. 

126 

(«)  ib)  (c) 


P^ 


(m 


^$9- 


r 


la- 


m 


ltii& 


i2g: 


-\>^ 


.^ 


I  7 
#5 


-r 


b7 
b5 


r 


At  (a)  the  chord  Bb,  E,  G,  C,  when  arranged  in  its  fundamental 
position  C,  E,  G,  Bb,  is  seen  to  contain  the  intervals  of  a  major  3d, 
perfect  5th,  and  minor  yth,  and  is  therefore  an  inverted  D^  chord, 
whose  fundamental,  during  the  life  of  that  chord  at  least,  is  the 

A  A 

Dominant  of  the  key  of  F  or  f. 

43 


44 


CUMULATIVE   HARMONY 


At  (b)  the  chord,  when  arranged  in  its  fundamental  position,  in- 
dicates  B  as  a  Dominant,  and  is  consequently  in  the  key  of  E  or  e. 

At  (c)  the  rearrangement  of  the  chord  indicates  a  Dominant  Db, 
therefore  a  Tonic  Gb,  and  this  occurs  with  a  signature  indicating  the 
key  of  C  or  a. 


Resolution  of  the  D^  Chord 

The  D^  chord  is  generally  followed  by  the  T  triad,  to  which  it  re- 
solves. The  combination  of  T  triad  preceded  by  the  D  chord 
forms  the  authentic  cadence,  which  will  be  considered  at  length  under 
the  head  of  cadences. 

By  resolution  is  meant  the  progression  of  the  various  voice  parts 
from  a  dissonant  chord,  or  chord  of  motion,  to  a  consonant  chord,  or 
one  of  repose. 

A  note  dissonant  with  its  fundamental  may  not,  as  a  rule,  be  doubled. 
Its  dissonant  character  gives  it  exceptional  prominence,  in  addition 
to  which,  notes  with  compulsory  resolution  would  if  doubled  be 
likely  to  cause  faulty  parallels. 


127 


(a) 


(^) 


(O 


(^) 


D7    T3 


U3 


1)5   T«    D5    T3    D5    T5    D5    Ts 


D8     T5 


In  all  forms  of  chords  of  the  yth,  the  yth  itself  has  a  natural  tend- 
ency to  progress  downward  one  degree;  this  is  notably  true  of  the 
D',  which  inclines  persistently  to  the  T^  in  its  resolution  (a). 

The  D^,  by  reason  of  its  proximity  to  the  T^  and  its  isolation  from 
the  T^,  is  almost  as  strong  in  its  tendency  upward  one  degree  to  the 
T^;  for  this  reason  it  is  known  as  the  leading  tone  (b). 

Because  of  the  urgency  in  the  progression  of  these  two  members 
of  the  D^  chord,  known  as  the  sensitive  tones,  they  are  said  to  have 
compulsory  resolution,  and  may  not   be   doubled,  as,  in  additi' 
their  distinctive  prominence   in    the    chord,   faulty  parallel? 
probably  result. 


THE    DOMINANT    SEVENTH    CHORD 


45 


With  the  tendency  of  all  members  of  the  D  chord  toward  finah'ty, 
the  D^  inclines  distinctly  to  the  T*,  which  may  be  said  to  be  its  note 
of  resolution;  for  melodic  purposes,  however,  it  very  frequently 
proceeds  to  the  T^,  in  which  case  the  D^  should  be  omitted,  in  order  to 
prevent  a  doubling  of  the  T^  in  the  succeeding  chord.  It  may  also 
proceed  to  the  'P  for  melodic  purposes,  or  to  aid  in  forming  accompani- 
ment figures.  For  these  reasons  the  D^  is  said  to  have  optional  reso- 
lution (c). 

While  the  D^  is  occasionally  retained  with  this  progression  of  the 
D^,  and  the  T'  doubled  in  the  resolution,  the  student  is  cautioned 
against  such  modes  of  procedure  as  will  result  in  a  doubled  3d,  in 
any  case  for  the  present,  and  until  it  may  be  done  advisedly. 

Following  the  rule  applied  to  chord  connection  in  the  triads,  the 
D*,  being  a  tone  common  to  both  chords,  is  retained  in  the  same  voice, 
becoming  the  T^  {d). 

From  the  above  details  we  form  the  following  table  of  resolutions 
of  the  D^  chord  to  the  triad  of  the  Tonic: 

The  D^  resolves  to  the  T'. 

The  D^  resolves  to  the  T^. 

The  D^  resolves  to  the  T^  or  Tl 

The  D^  is  retained  as  a  tone  common  to  both  chords  and  becomes 
the  T^ 

In  the  fundamental  position  of  this  chord  the  student,  for  the 
present,  should  omit  the  D-'  and  double  the  D  fundamental,  in  order 
to  obtain  a  complete  triad  in  the  resolution. 


128 

(«) 

f) 

'  y 

^-— .              II 

/\                   <*T  — -  f^f^                 1  1 

im      ^.^^            II 

\\) 

<^ — -  ^ 

< 

/m\'                                        II 

IP-'*                                         1 1 

\K~^                   'V           t\ 

"         fi>                 u 

At  (a)  the  complete  D^  chord,  consisting  of  four  different  notes, 
when  strictly  resolved,  leads  to  an  incomplete  triad  of  the  Tonic 
2^1  ^^ining  but  two  different  notes,  C  and  E,  thus  resulting  in  an  un- 
lance  of  the  harmonic  content  of  the  two  chords.     The  follow- 


Domina 


r  the  present,  preferred: 


46 


CUMULATIVE   HARMONY 

120 


/ 

/ 

/ 

/'        ^-— -A- 

1 

f( 

V 

V 

^      «;«=*' — g 

'^        ^ 

< 

o 

^^^ 

i 

S^' 

<© <5^ 

( 

pj. 

1 

V>^                       <V 

O 

M 

1 iS>— = 1 

— «-— == " 

Here,  it  will  be  observed,  the  Dominant  and  Tonic  chords  each 
contain  three  different  notes,  resulting  in  a  better  balance  between 
the  two  chords. 

The  D^  chord  may  at  times  retain  its  four  notes  complete,  the  5th 
ascending  to  the  5th  of  the  Tonic  for  resolution. 


-s^ 


The  D''  is  classed  as  an  intensifying  chord.  By  intensification  is 
meant  the  use  of  chords  with  compulsory  resolution.  This  subject 
will  receive  more  extended  comment  in  another  chapter. 

It  may  be  stated  in  this  connection  that  while  with  certain  con- 
ditions (to  be  made  clear  in  a  subsequent  chapter)  the  7  th  may  be 
doubled,  it  is  absolutely  forbidden  to  double  the  leading  tone  in  any 
circumstances,  except  when  necessary  in  order  to  preserve  a  harmonic 
or  melodic  figure  in  sequence. 

Work  out  the  following  exercises  in  various  keys  as  before.  In 
the  D^  chords  omit  the  5th  and  double  the  fundamental. 


181 

1 

1 

/m\'             1             1 

fy                   . 

1 

1 

1 

lCJ'/» 

1 

^\ 

fj         1 

A-       ^ 

Kl^X  ,      r^           -^ 

1 

rj 

.^                             1 

1 

f> 

>-^               1 

1 

L ^ 1 

-<&' 

1 

s 


3 


#6 
4 


#6 
4 


-«a- 


I 


THE   DOMINANT    SEVENTH   CHORD 


47 


132 


S 


^ 


-rs- 


-s>- 


b6 


l>7 


I 


-*a — r-i 


These  exercises  may  be  employed  to  form  harmonic  plans  for 
accompaniments,  over  which  melodies  are  to  be  constructed,  as  be- 
fore. It  may  be  stated  that  where,  for  the  sake  of  good  voice  pro- 
gression, a  member,  of  the  chord  has  been  omitted  (as  the  D^)  in  the 
fundamental  position  of  the  D^  chord,  such  notes  may  be  freely  in- 
cluded among  those  available  for  use  in  the  melody. 

Play  all  these  exercises  and  examples,  and  have  them  played. 


in.  No.  5 


(pl 


Wagner,  "  Elsa's  Dream  " 


-U 


-zsts'- 


r 


Pag 


-6^ 

-19- 


lU.  No.  6 


McCoy,  "  Dance  of  the  Fireflies  " —  Cave  Man 


The  harmonic  scheme  is  shown  at  (a). 


CHAPTER   IX 


INVERSIONS   OF  THE  D^  CHORD 

The  D^  chord,  containing  four  different  notes,  is  susceptible  to 
three  inversions. 

The  first  inversion  places  the  third  from  the  fundamental  in  the 
bass,  the  other  members  of  the  chord  forming  the  intervals  of  a  3d, 
5th,  and  6th;  figured  f,  the  figure  3  being  omitted  for  the  sake  of 
brevity.  As  the  D^  has  a  compulsory  resolution  to  the  T^,  this 
position  is  to  be  followed  by  the  Tonic  triad  in  fundamental  position. 


133 


(a) 


{b) 


(^). 


{d) 


-y^ 


-Tb^- 


<^^- 


-"&- 


z^- 


±g 


^S^^l 


[W- 


-«»- 


-s*- 


1T 

5 


i^ 


be 
b5 


t>5 


At  (a)  is  an  example  of  the  first  inversion  of  the  D^  chord,  the 
fundamental  of  which  is  G,  with  B  as  the  bass,  and  is  followed  by 
the  Tonic  triad  on  C.  At  (&)  is  the  first  inversion  of  the  D^  chord  on 
A,  with  C^  as  the  bass.  At  (c)  the  first  inversion  of  the  D^  chord  on 
Eb  requires  a  chromatic  alteration  of  each  of  the  interval  figures;  and 
at  {d)  the  3d  from  the  actual  bass,  F#,  is  indicated  by  the  sharp 
alone.     In  each  case  the  chord  is  resolved  into  its  Tonic  triad. 

The  second  inversiott  places  the  D^  in  the  bass,  the  other  members 
of  the  chord  forming  the  intervals  of  a  3d,  4th,  and  6th;  figured  3, 

As  the  D^  has  optional  resolution,  this  position  of  the  chord  may  be 

followed  by  the  T  triad  in  fundamental  position,  observing  the  given 

rules  for  resolution  of  the  D^  chord ;  or  it  may  be  followed  by  the  first 

inversion  of  the  T  triad,  in  which  case  the  D^  should  be  omitted  (in 

order  to  prevent  faulty  doubling  of  the  T^),  and  the  chord  of  |  used 

instead  of  3. 

48 


INVERSIONS   OF   THE   D^   CHORD 


49 


134 


('») 


(^) 


i 


=t 


(0 


^=^ 


C'/) 


=^^ 


^ 


:?2- 


«ss^- 


izg: 


^: 


{m 


i 


ii^ 


:|^ 


TT 


:12^ 


^6 
4 
3 


'-rb4 
b 


b5 


#6 
4 
3 


^m 


(J) 


U) 


ih) 


M- 


±^ 


^ 


^^ 


1=^ 


m 


li^ 


-ii— )- 


-m 


^ 


b4 


b6 


S6 
4 


At  (a)  is  the  second  inversion  of  the  D^  chord  on  G,  with  D  as  the 
bass;  the  other  members  of  the  chord  forming  the  intervals  of  a  3d, 
4th,  and  6th;  figured  3.  At  (b)  is  the  second  inversion  of  the  D^ 
chord  on  A,  with  E  as  the  bass,  and  the  rest  of  the  chord  represented 
by  the  figures  4 .  At  (c)  is  the  second  inversion  of  the  chord  of  Eb 
and  at  (d)  the  second  inversion  of  the  chord  of  B,  each  of  which  is  fol- 
lowed by  its  corresponding  T  triad. 

At  (e),  (/),  (g),  (h),  the  second  inversions  of  the  same  D  chords  are 
given,  with  the  D^  omitted  in  order  to  avoid  doubling  the  3d  in  the 
resolution  to  the  T  chord. 

The  following  exceptional  resolution  may  be  noted,  which  may  be 
occasionally  employed  to  good  effect: 

When  the  second  inversion  of  the  D^  chord  is  followed  by  the  first 
inversion  of  the  T  chord,  the  D'^  may  resolve  by  degree  upward  to 
theT^ 

135 


r 


f=r 


-r^ 


-«»- 


4  6  4  6 

3  3 

This  is  given  primarily  to  aid  in  analysis. 


50 


CUMULATIVE    HARMONY 


The  third  inversion  places  the  D'  in  the  bass,  the  other  members  of 
the  chord  forming  the  intervals  of  a  2d,  4th,  and  6th,  the  figuring 
abbreviated  to  2  or  2. 

As  the  7  th  has  a  compulsory  resolution  downward  one  degree  to 
the  T^,  this  position  of  the  chord  is  to  be  followed  by  the  first  inversion 
of  the  T  triad. 


136 


(«) 


{b) 


ic) 


id) 


i 


is 


IS 


^ 


f^ 


to 


w 


-s>- 


m\ 


^EL 


:¥ 


-Ki- 


tt* 

6 

"r-be 

'  b6 

'#6 

2 

'      4 

b2 

b 

#4 
2 

Here  we  have  the  third  inversion  of  the  four  D^  chords  given  in  the 
preceding  example,  with  the  D^  in  the  bass  resolving  to  the  T^,  and 
with  the  T  chord  in  its  first  inversion. 


Weber,  "  Euryanthe  " 


The  student  should  transpose  the  following  exercises  to  many 
different  keys,  and  work  out  in  all  the  different  forms  that  have  been 
given. 

137 


-7^ 


7r3 ^ TTS 6" TTi 

^a — ~xl 1 ^^ rfEJ ^£i. 


a     e*. 


^^  g*> 


[m 


-ri- 


:^-^ 


-s*g- 


«5^ 


u 


-Ki- 


■^^ 


-ir^ 


-r^ 


-^ 


S6 
4 
3 


1^6 
4 


-^'-tTg^ 


INVERSIONS   OF   THE   D^  CHORD 


SI 


i^:^ 


i?: 


zz: 


I 


1^ 


i^ 


-Of 

6 
b5 


138 


^ 


-Z5I- 


St^ 


;a=s^ 


m 


6 
b5 


g 


^ 


5 


#4 
2 


S6 
4 
3 


6 
5 


S6 
4 
3 


139 


m 


^ 


i^ 


^ 


i;6 

4 

3 


I 


£ 


te: 


■75^ 


75^ 


S6 
4 
3 


140 


n^ 


±^ 


^ 


-z?- 


I^ 


4      6 
2 


S6 

4 
3 


E^^ii^ 


--1 — r 


I 


:p: 


3^ 


i;6 

4 
8 


2 


3 


-75*- 


141 


m 


14: 


75—-* !«!S^-P^ ^ 


:#^ 


:2± 


b±^^ 


i 


Br^^^hdi 


m 


b      #6 
4 


if6 

4 


52 


CUMULATIVE    HARMONY 


142 


m 


-T^ 


^ — (S- 


m 


6 

b5 


#6 
4 
3 


4        6 
3 


I 


^^—^ 


-(=2 ^- 


5 


-s*- 


143 


^■^ 


I3E 


i^-"-^ 


-75^ 


6         4 
3 


«4 
2 


6         6  7 

4  S 


-.5*- 


:f 


—75^ 


b6 


6 

b5 


Additional  attention  will  be  directed  to  the  D^  chord  in  a  subsequent 
chapter. 
Play  all  these  exercises  and  examples,  and  have  them  played. 


CHAPTER   X 
SERIAL   MODULATIONS 

A  modulation  is  a  change  of  key  without  a  change  of  signature,  and 
is  generally  transitory. 

Modulation  is  effected,  melodically ,  by  chromatic  elevation  or  de- 
pression of  one  or  more  members  of  the  diatonic  scale  based  upon  one 
Tonic,  in  such  manner  as  to  form  a  correct  diatonic  series  based  uf)on 
a  different  Tonic. 


144 


i 


(«) 


(^) 


!  g 


^?=ac? 


*? 


i 


(c) 


:^^ 


^-^=^ 


(^) 


I 


tl5^ 


J-tb! 


-^— ^- 


::r 


(O 


{/) 


^^ 


b^    * 


I 


^E^S 


■^— ^ 


At  (a)  is  given  the  accepted  form  of  the  diatonic  major  scale  — 
based  upon  the  Tonic  C.  At  (b)  the  diatonic  succession  is  archi- 
tecturally identical,  with  half-step  successions  between  3-4  and  7-8, 
based  upon  the  Tonic  G.  This  involves  the  chromatic  elevation  of 
F  to  F?^. 

In  like  manner,  at  (c),  by  chromatic  depression  of  B,  a  major  dia- 
tonic scale  is  formed  with  F  as  the  Tonic. 

At  (d),  (e),  and  (/)  are  examples,  in  similar  manner,  of  the  scale  of 
a  and  the  modulated  scales  to  the  directly  related  keys,  e  and  d. 

Modulation  is  effected  harmonically  through  the  introduction  of 
the  D  chord  of  a  foreign  key. 

53 


54 


145 


{a) 


CUMULATIVE   HARMONY 


M 


^ 


-m 


^ 


g^ 


1^ 


3 


z?- 


J2Z 


b7 


At  (a),  by  the  introduction  of  the  D^  chord  on  D,  a  modulation 

A 

to  the  key  of  G  is  effected. 

A 

In  like  manner,  at  (b)  occurs  a  modulation  to  F,  and  at  (c)  a  modu- 
lation by  the  Dominant  triad  on  E  to  the  key  of  a. 

Attention  will  be  directed,  for  the  present,  to  harmonic  modu- 
lations. 

The  harmonic  modulations  in  the  following  six  forms  should  be 
worked  out  serially.  Other  forms  of  modulation,  as  well  as  deviations 
from  these,  will  be  given  later. 

Modulation  in  each  form  should  proceed  serially,  until  the  tonality 
represented  by  six  flats  or  six  sharps  is  reached,  at  which  point  the 
enharmonic  change  (without  modulation)  should  be  made,  and  the 
modulations  continued  as  before,  until  a  return  to  the  original  key  is 
accomplished,  thus  completing  the  circle  in  that  form  of  modulation. 
By  enharmonic  change  is  meant  different  notation  for  the  same 
tones;  for  example,  B#,  C,  Dbb  represent  the  same  tone.  The  en- 
harmonic change  from  the  key  of  Gb  is  to  F#. 

Rule  I.  Take  the  Tonic  for  a  new  Dominant,  proceeding  from 
major  to  major,  and  from  minor  to  minor. 


146 


i 


im 


-T^ 


l^E^ 


%^- 


b7 


A 


n Kt 


b7 


etc. 


enharmonic  change 


A 

G> 


b7 


b5 


etc. 


SERIAL   MODULATIONS 


55 


Beghining  with  the  key  of  C  and  following  Rule  I,  we  select  the 
Tonic  C  for  a  new  Dominant.  By  building  a  D^  chord  consisting  of 
C,  E,  G  (omitted)  and  Bb  upon  it,  that  note  becomes  a  Dominant, 
which  resolves  to  its  corresponding  Tonic,  F. 

Again,  selecting  the  Tonic  F  for  a  new  Dominant,  by  the  same 

A 

mode  of  procedure  we  accomplish  a  modulation  to  the  key  of  Bb. 
Continue  in  this  manner  through  keys  of  major  gender,  until  the 

A 

key  of  Gb  (represented  by  a  signature  of  six  flats)  is  reached,  at 
which  point  the  enharmonic  change  (without  modulation)  to  the  key 
of  Fir  is  made. 

Modulation  should  then  proceed  in  similar  manner  until  a  return 

A    ^ 

to  the  initial  key  of  C  is  accomplished. 


m.  No.  8 


Beethoven 
"  Symphony  I 


i^ 


* 


-^ — *- 


m 


fp 


~^ 


A  A 

*  Modulate  from  C  to  F. 


In  like  manner  by  the  same  rule,  the  keys  of  minor  gender  modulate 
to  minor. 

enharmonic  change 


147 


A 

eb 


'V 


A 


fe^ 


ri 


r^^ 


g^^ 


-f^— tg 


tXS 


*2 


■■:$^m. 


etc. 


i 


g 


etc 


3 


5 


i^ 


=^ 


b7 


b5 

b 


#5 


Beginning  with  the  key  of  a,  and  following  the  rule  by  taking  the 

A 

Tonic  A  for  a  new  Dominant,  we  modulate  to  the  key  of  d;   thence 
by  the  same  means  to  g,  and  continuing  until  the  key  of  eb  is  reached. 


56 


CUMULATIVE   HARMONY 


By  making  the  enharmonic  change  to  d#  and  continuing  as  before, 
we  finally  return  to  the  initial  key  of  a,  thus  completing  the  circle, 
proceeding  from  minor  to  minor. 

m.  No.  9  MOSCHELES 

"  Study  in  C#  Minor  " 


=#i 


m 


m^. 


^¥IB^ 


^£=%=i=*g 


^ 


From  c#  to  f#. 

Rule  II.    Take  the  supertonic  for  a  new  Dominant,  proceeding 
from  major  to  major,  and  from  minor  to  minor. 


148 


A 


"V" 


Gb 


i 


Ife 


^ 


-?^- 


-^ 


fe=l 


's»- 


f^ESS 


■^1^=^^? 


-25l- 


:|^ 


^'^-- 


« 


-K 


b7 


b5 

b 


Beginning  with  the  key  of  C,  taking  the  supertonic  D  for  a  new 

A 

Dominant,  we  modulate  to  G,  thus  resolving  to  a  major  triad  in  con- 
formity to  the  requirements  of  the  rule.     As  the  supertonic  in  the 

A      _ 

key  of  G  is  A,  this  note  in  turn  is  selected  for  the  next  Dominant, 

A 

effecting  a  modulation  to  the  key  of  D,  etc. 

m.  No.  10 

Schumann,  op.  21,  No.  i  —  Novellette 


m 


t 


^\^_rj^4^ 


4=*= 


^ 


:S-^^ 


s^ 


r 


A  A 

From  F  to  C. 


r   ^    f 


^s^ 


r 


SERIAL   MODULATIONS 


57 


Also  by  Rule  II  —  from  minor  to  minor  —  we  commence  with  the 

A 

key  of  a  and  modulate  to  e,  thence  to  b,  etc. 


149 


S 


t^^ 


-¥ 


fc 


etc 


12- 


iJ5 


Rule  III.    Take   the   mediant   for  a  new  Dominant,  proceeding 
from  major  to  minor,  and  from  minor  to  major. 


150 


n 

A 

c 

J 

A 
a 

1 

1 

1 

1 

f        A 

1 

1    ;            -^           ' 

t^T-ir- 

-|i^— ^= 

—^^9— 

-r- 

w—^— 

Sf — 

& 

-^ 

etc. 

fm\'            i 

, 

1 

K^' 

(^ 

[ 

Kly         ^ 

^                    \ 

1         ^ 

\ 

7 

b7 

ej 

Beginning  as  before  with  the  key  of  C,  and  selecting  the  mediant 
E  for  a  new  Dominant,  we  effect  a  modulation  to  a,  conforming  to 
the  requirements  of  this  rule  in  proceeding  from  major  to  minor;  as 
the  mediant  in  the  key  of  a  is  C,  that  note  is  selected  for  a  new  Domi- 

A 

nant,  with  a  modulation  to  F.     Continuing  after  this  plan  until  the 

A 

key  of  Gb  is  reached,  the  enharmonic  change  is  made,  followed  by  the 

A 

return  to  C. 

As  the  minor  keys  obtainable  by  this  rule  are  included  in  the  above, 
the  student  will  not  be  required  to  use  a  as  an  initial  key. 


58  CUMULATIVE    HARMONY 

111.  No.  11 

Schubert,  "  Unfinished  Symphony  in  B  Minor  " 


^ 


-s*- 


-^ —       m 


A. 


1^ 


is 


m 


3 


A  A 

From  b  to  G. 


Play  all  these  exercises  and  examples  and  have  them  played. 


CHAPTER  XI 

SERIAL  MODULATIONS.     (Continued) 

Rule  IV.   Take  the  Subdominant  for  a  new  Dominant;   major  to 
major  (a),  and  minor  to  minor  (b),  also  singly,  minor  to  major  (c). 

151 

A  A  A  A 

C  Bb  a  g  not  serially 


n 


^i 


^ 


M 


M- 


h^     g" 


ia) 


{b) 


etc. 


m-: 


ic) 


V=^t 


b7 


The  student  should  also  commence  with  the  keys  of  F  and  d,  by 
this  rule,  to  reach  a  number  of  keys  not  included  in  the  circle  when 

^        A  ^ 

the  initial  key  is  C  or  a. 

162 


A, 


a      ^^f^    ,  ft 


#=sl 


te: 


A 

d 


I^ 


b7  1>5 


t^ 


'■^^^ 


lit 


etc. 


3 


m.  No.  12 


?5l_^- 


Chopin,  "  Mazurka,"  op.  56,  No.  2 


-# — ^- 


=s=P 


*?=it=*=^ 


?:      1?: 


*'&^ 


-ff*         I* 


¥ 


m 


I*    I* 


^4=5 


^ 


A  A 

EtoD. 


59 


6o 


CUMULATIVE   HARMONY 


Rule  V.   Take  the  submediant  for  a  new  Dominant;   major  to 
minor,  minor  to  major. 


Beginning  with  the  key  of  C  and  proceeding  from  major  to  minor, 

A 

we  reach  the  key  of  d.     As  the  signature  of  that  key  is  one  flat,  the 
submediant  would  necessarily  be  Bb,  which  is  the  note  to  select  for 

A 

the  new  Dominant,  effecting  a  modulation  to  Eb. 

A 

The  student  may  also  use  F  as  the  initial  key. 


m.  No.  13 


Chopin,  "  Nocturne,"  op.  15,  No.  2 


A  A 

n  to  gs. 


Rule   VI.    Take   the   sub  tonic  for  a  new  Dominant;   major   to 
minor,  minor  to  major. 


With  C  as  the  initial  key,  we  select  the  subtonic  B  for  the  new 
Dominant,  modulating  to  e.  As  the  signature  of  e  is  one  sharp,  the 
subtonic  in  that  key  is  D,  which  is  the  note  to  select  for  a  new  Domi- 
nant. 


SERIAL    MODULATIONS 


6i 


m.  No.  14 


— ^-n 

Chopin,  "  ] 

'^locturne,"  op. 

15,  No.  3 

-&T^ i- 

'-<'— — 1 

r-^— — 1 

~v 

W'l  r  r  r~' 

-H 

-1 

^ 

_j 

-*— 

«     1 

^- 

A  A 

From  g  to  Bb. 


Let  the  student  clearly  understand  that  it  is  not  the  3d  in  the 
D^  chord  (the  subtonic  elevated  to  serve  as  a  leading  tone)  that  is 
indicated  as  the  note  for  selection  by  this  rule  for  the  new  Dominant. 

The  7  th  of  the  scale  in  the  minor  mode  is  required  to  be  raised 
chromatically  when  it  forms  a  part  of  the  D^  chord  in  order  that  the 
3d  in  that  chord  shall  be  major,  but  this  fact  in  no  wise  affects  its 
scale  existence  for  serial  modulation,  which  must  conform  absolutely 
to  its  signature  indication. 

Chromatic  alterations  of  the  7th  and  6th  of  the  scale  for  melodic 
u^s  will  be  discussed  later. 

For  the  purpose  of  acquiring  a  thorough  familiarity  with  the  various 
inversions  of  the  D^  chord  and  their  resolutions  to  the  Tonic,  the 
student  should  review  the  preceding  modulations  (or  at  least  a  con- 
siderable part  of  them),  using  the  D^  chord  with  its  resolution  not 
only  in  its  fundamental  position,  but  in  all  its  inversions. 

In  order  that  they  will  appear  in  the  most  agreeable  succession, 
the  third  inversion  may  be  used  first,  to  be  followed  by  the  second 
and  first.  Care  should  be  taken  to  resolve  each  member  of  the  chord 
in  accordance  with  the  rules. 


155 
Rule  I 


F     D 


D 


D 


D 


^?=r=i 


:^ 


^^- 


:^ 


S 


(m 


-Z>^zr 


-12^ 


6 
b5 


62 


CUMULATIVE   HARMONY 


By  Rule  I  —  taking  the  Tonic  for  a  new  Dominant  —  the  modu- 
lation with  the  D  chord  in  fundamental  position,  as  already  used,  ap- 
pears first;  following  this  the  third  inversion  of  the  same  chord  with 
the  D^,  Bb,  in  the  bass,  resolving  to  the  T^  in  the  succeeding  chord; 
next  the  2d  inversion  of  the  same  chord  resolving  to  fundamental 
position,  and,  finally,  the  first  inversion  similarly  resolved.  This  com- 
pletes one  modulation.  ^ 

By  this  rule  the  succeeding  key  is  Bb,  in  which  the  same  plan 
should  be  followed. 

The  student  is  advised  to  do  this  work  by  several  of  the  rules,  and 
in  both  major  and  minor  genders. 


CHAPTER  XII 
DIRECTLY  RELATED   KEYS 

The  directly  related  keys  to  any  given  key  are  those  that  may  be 
represented  by  the  same  signature,  or  by  one  sharp  or  one  flat  more 
or  less;  also  the  Tonic  minor  of  a  major  key  and  the  Tonic  major  of  a 
minor  key.  ^ 

Hence,  the  directly  related  keys  to  C,  with  the  corresponding 
rules  for  modulation  through  which  they  may  be  reached,  are  as 
follows: 

A  ^  A 

By  the  same  signature,  a;   bv  one  sharp  more,  G  and  e;   by  one 

A  A  '    .  .  A 

flat  more,  F  and  d  and  the  Tome  mmor,  c.     As  a  signature  of  one 

A     ^ 

sharp  or  one  flat  less  than  that  of  C  is  obviously  impossible,  they  are 
not  considered. 

A 

F,  modulation  bv  Rule  I; 

A 

G,  modulation  by  Rule  H; 
a,  modulation  by  Rule  IH; 

A 

d,  modulation  by  Rule  V; 

e,  modulation  by  Rule  VI; 

and  the  Tonic  minor  key  of  c  with  the  same  Dominant. 
In  like  manner,  those  directly  related  to  the  key  of  a  are: 

A  '^  A 

By  the  same  signature,  C;   by  one  sharp  more,  G  and  e;  by  one 

A  A 

flat  more,  F  and  d  and  the  Tonic  major,  A. 
One  sharp  or  one  flat  less  are,  of  course,  not  considered. 

A  ^ 

d,  modulation  by  Rule  I; 

e,  modulation  by  Rule  II; 

A 

F,  modulation  by  Rule  HI; 

A 

G,  modulation  by  Rule  IV: 

A 

'  C,  modulation  by  Rule  VI; 

A 

and  the  Tonic  major  key  of  A  with  the  same  Dominant. 

63 


64 


CUMULATIVE   HARMONY 


The  ones  most  closely  allied  among  indirect  modulations  are  those 
by  Rule  IV  from  major  to  major,  and  Rule  V  from  minor  to  major. 

Thus  from  C  and  a,  by  these  two  rules  the  indirect  modulation  to 

A  -. 

Bt>  is  attained  in  both  cases. 

Indirect  modulations  are  frequently  effected  by  combinations  of 
two  or  more  different  rules. 

A  ^ 

In  order  to  modulate  from  the  key  of  C  to  g,  Rules  I  and  V  may  be 
used  in  combination,  thus: 

156 


i^ 


^^ 


^ 


-j^ 


S' 


-^ 


b7 


A  A 

To  modulate  from  G  to  F,  Rules  V  and  III  are  employed,  thus: 


157 


l=± 


III 


:^^ 


-1^ 


:^i^ 


-s^ 


:H^ 


-s^ 


-6h 

7 


Modulations  are  frequently  effected  through  a  repetition  of  the 
same  rule. 


158 


DIRECTLY   RELATED   KEYS  6$ 

A  A      ^ 

Here,  by  repetition  of  Rule  II,  a  modulation  from  C  to  D  is  ac- 
complished. 

By  what  rules  or  combination  of  rules  would  the  following  modu- 
lations be  accomplished: 

A  AA  AA  AA  a-^  AA  a^  a'^A 

C  to  Bb,  C  to  F,  C  to  G,  G  to  e,  G  to  F,  F  to  g,  F  to  a,  C  to  e, 

A  AA  A^  AA  a'^  AA  A 

G  to  b,  D  to  a,  d  to  C,  F  to  e,  Bb  to  Ab,  A  to  b? 

The  instructor  should  add  many  other  modulations  by  combination 
of  two  or  three  rules,  all  of  which  should  be  thoroughly  expounded, 
both  orally  and  by  writing. 

The  following  oral  practice  should  accompany  the  above: 

Modulating  from  C  by  Rule  I,  what  key  would  be  reached?  By 
Rule  II?  III?  IV?  V?  VI? 

Modulating  from  A  by  Rules  I  and  II?  Ill  and  IV?  V  and  VI? 


CHAPTER   XIII 
HARMONIZATION  OF   MELODIES 

From  this  point  the  practice  of  harmony  will  continue  under  given 
melodies. 

The  entire  scheme  of  harmonization  of  melodies  will  be  conducted 
through  the  use  of  the  three  primary  notes,  the  Tonic  [T],  Sub- 
dominant  [S],  and  Dominant  [D],  and  their  chords  in  various  forms; 
and  it  may  be  stated  here  that  the  scope  of  this  three-point  mode  of 
harmonization  will  include  the  employment  (as  tributaries  of  these 
chords)  of  all  harmonies  to  be  found  in  the  works  of  the  standard 
composers,  together  with  their  progressions  and  general  treatment. 

The  student  will,  for  a  time  at  least,  place  the  primary  initials  T, 
S,  D,  in  capitals  above  the  notes  of  melody,  to  aid  in  selecting  de- 
sirable basses,  and  to  assist  in  subsequent  analysis. 

Rule  I.  Harmonize  the  first,  third,  or  fifth  of  the  scale  with  the 
Tonic  [T]  (a),  the  fourth  or  sixth  with  the  Subdominant  [S]  (b),  and 
the  second  or  seventh  with  the  Dominant  [D]  (c) , 


159 


T 

T 

1 

z^ 

T 

1 

S 

^ \ 

S 

D 

D 

iS 

te— J 

0- 

1 

-P- 
1 

(a) 

\ 

— 1 

— 1» 

1 

{a) 

r 

-»■- 

1 

p- 

m 
1 

{b) 

p 

— p 

p 

— p 

\!^_^ 

1 

^ 

1 

1 

The  7th  should  be  used  in  the  Dominant  chord  when  it  is  followed 
by  the  Tonic,  unless  its  use  causes  a  doubling  of  the  T^  in  the  reso- 
lution, in  which  case  the  7th  should  be  omitted. 

66 


HARMONIZATION   OF   MELODIES 


67 


3= 


:it: 


^ 


At  (a)  the  given  melody  moves  from  the  second  of  the  scale  to  the 
third,  that  is,  from  the  D*  to  the  T^;  as  the  D^  [F]  has  a  compulsory 
resolution  it  must,  of  necessity,  resolve  to  the  T^  [E],  causing  an  un- 
desirable doubling  of  that  note.  At  {b)  the  D^  has  been  omitted,  the 
complete  triad  of  the  Dominant  progressing  regularly  to  the  triad  of 
the  Tonic,  without  the  offending  doubled  3d. 

An  example  of  a  melody  harmonized  as  directed  above,  using 
fundamental  basses  only,  and  adding  the  7th  to  the  Dominant  triad 
when  it  can  be  done  without  doubling  the  3d  in  the  resolution  to  the 
succeeding  Tonic  triad,  is  here  given. 

161 

{a)        {b)        {c)       {d)        ^e)        (/)        U)  {h) 


D 


D 


^ 


^ 


4. 


^=i 


J=i 


S 


:S5: 


5=2^=13; 


=2 


3 


-Z5t 


^^ 


-^ 


-K^ 


ES 


-77 


D 


D 


D   {h)   T 


D 


i 


^ 


T 


^^^i 


3 


12^ 


-^!9i 


-^. 


-s»- 


g 


3 


D 


D 


:i 


D 


7 


^^ 


■^ 


% 


7 


sir 


68  CUMULATIVE    HARMONY 

At  (a)  the  first  of  the  scale,  C,  is  harmonized  with  the  Tonic,  C, 
the  triad  of  which  is  C,  E,  and  G,  with  C  in  the  soprano,  and  G  and  E 
assigned  to  the  alto  and  tenor  in  a  position  as  near  the  soprano  as  is 
possible.     We  have  thus  properly  harmonized  the  initial  note. 

At  (b)  the  seventh  of  the  scale  is  harmonized  with  the  Dominant, 
G.  As  the  D^  chord  is  G,  B,  D,  and  F,  it  follows  that  with  the  D^ 
omitted  and  the  B  already  in  the  soprano,  the  doubled  G  and  the  F 
would  be  available  for  the  alto  and  tenor.  As  the  G  is  the  note  com- 
mon to  this  and  the  preceding  chord,  it  should  be  retained  in  the 
same  voice  (the  alto),  thus  leaving  the  seventh,  F,  for  the  tenor. 

At  (c)  the  common  note  G  is  retained  in  the  alto,  and  the  D^  re- 
solved to  the  T^  in  the  tenor. 

As  the  melody  note  at  (d)  proceeds  to  the  T^  at  (e),  it  is  obvious 
that  if  the  7th  should  appear  in  the  Dominant  chord  at  (d),  it  would 
demand  a  resolution  to  the  T^  at  (e),  thus  doubling  that  member  in 
the  latter  chord.  To  obviate  this,  the  7th  is  omitted,  and  the  D  triad 
used  instead. 

As  the  note  common  to  the  two  chords,  G,  is  in  the  alto,  the  re- 
maining note  B  is  assigned  to  the  tenor,  thus  placing  the  chord  in 
open  (or  dispersed)  position,  as  are,  by  natural  progression,  the  next 
six  chords. 

At  (/)  the  fourth  of  the  scale  is  harmonized  with  the  Subdominant, 
the  note  common,  C,  being  retained  in  the  tenor.  At  (g)  the  fifth 
of  the  scale  is  harmonized  with  the  Tonic;  in  order  to  retain  the 
note  common  in  the  tenor,  the  alto  descends  a  4th  to  E,  a  distance 
of  more  than  an  octave  between  it  and  the  soprano  note,  G. 

This  distance  is  lessened  in  the  next  chord. 

At  (h)  are  applications  of  the  following  rule: 

When  the  second  of  the  scale  is  followed  by  the  first,  the  D^  in  the 
fundamental  position  of  the  D^  chord  may  be  omitted  and  the  funda- 
mental doubled,  thus  assuring  a  complete  triad  in  the  resolution. 

The  omission  of  the  3d  from  the  Dominant  is  always  of  a  passing 
or  temporary  character,  and  should  never  occur  in  the  penultimate 
chord,  the  following  solution  being  preferred: 

When  the  D^  chord  is  in  fundamental  position,  the  D^,  if  it  occurs 
in  the  alto  or  tenor,  may  descend  to  the  T^,  resulting  in  a  complete 
triad  as  the  chord  of  resolution.  The  bass,  in  this  case,  should  move 
in  contrary  motion. 


HARMONIZATION    OF   MELODIES 


69 


162 


T         D 


i 


-$;         gj- 


4^A 


This  resolution  of  the  3d  of  the  Dominant  is,  at  times,  quite 
eflfective,  particularly  when  the  second  of  the  scale,  followed  by  the 
first,  appears  in  the  given  melody. 

Rule  II.  When  the  first  of  the  scale  is  repeated,  it  may  be  har- 
monized with  the  Subdominant. 

163 

T  s  T 


{W 


Rule  III.    When  the  fourth  of  the  scale  is  followed  by  the  third, 
the  fourth  may  be  harmonized  with  the  Dominant. 


164 


tj 


te 


D 


I^ 


4 


As  may  be  readily  seen,  the  fourth  of  the  scale  with  this  harmoni- 
zation is  the  7th  in  the  D^  chord,  duly  resolved  to  the  T^. 

It  is  not  to  be  assumed  that  this  rule  applies  to  all  cases,  as  the 
fourth  followed  by  the  third,  notably  in  the  cadence,  is  frequently 
harmonized  with  the  Subdominant. 

Harmonize  the  following  melody,  conforming  to  the  above  three 
rules;  transjwse  to  several  different  keys  and  harmonize. 


70 


CUMULATIVE   HARMONY 


165 


T      S       T      D 

(«)    {b)  {'c) 


TSDTDTSDTST 

{d)     {e)  if)  (^) 


AA 


-^    g; 


z:^-s! z?h-<» 


^ 


-■g^     ^ — g^ 


-^ — (^ 


:^ 


-fS' — ^ 


1^ 


J 


-J- 


lJ.  I 


etc, 


-^-^5^ 


^ 


r 


h.^  r  r  -M^r  -->  r-  J  r-  f  -^^-^-^-^- 

14  ^-J L_| L_^| ^_r_^^^^__l ^_i?^ 

At  (a)  the  first  of  the  scale  C,  repeated,  is  harmonized  with  the  Sub- 
dominant.  At  (6)  the  same  note,  again  repeated,  is  given  the  T 
harmony.  At  {c)  the  positions  in  the  chord  of  the  alto  and  tenor 
notes  are  changed  to  improve  the  voice  leading  and  bring  the  various 
voice  parts  to  better  relative  distances  from  each  other. 

At  {d)  the  fourth  of  the  scale  is  given  the  S  chord;  while  at  {e) 
the  fourth,  being  followed  by  the  third,  has  the  D  harmony. 

At  (/)  the  D^  descends  to  the  T^,  giving  better  relative  positions 
to  the  voice  parts  than  would  have  otherwise  been  the  case. 

At  (g)  the  positions  of  the  alto  and  tenor  have  again  been  changed 
within  the  chord  to  get  better  subsequent  voice  leading,  such  as 
avoidance  of  parallel  octaves  and  of  all  voices  moving  in  similar 
direction. 

Rule  IV.  The  fifth  of  the  scale  may,  at  times,  be  harmonized 
with  the  Dominant;  when  it  occurs  several  times  in  succession,  it 
should  be  harmonized  alternately  with  the  Tonic  and  Dominant, 
generally  selecting  the  Tonic  for  the  first  harmonization. 


166 


D 


-i 


r 


r^ 


_^ ^ 


t- 


HARMONIZATION   OF   MELODIES 


71 


This  harmonization  is  particularly  applicable  when-  the  fifth  of  the 
scale  is  followed  by  the  first  above  or  below,  in  which  case  the  T 
chord  of  resolution  is  generally  incomplete  by  its  5th  being  omitted, 
as  at  (a)  in  the  following  example,  unless  the  3d  in  the  alto  or  tenor 
descends  to  it. 


167 


^m 


(a) 


i^ 


^ 


li 


r 


^ 


I       I 


J 


^      0 


W^ 


? 


^ 


6  6  6 

'744 


6  6 

4 


^ 


1 1 1        ^    -g * 


3t=^ 


^ 


=P=F^ 


^ 


168 


i 


^^ 


0  0  -g 


m      F- 


^ 


^^^ 


f'  ■    »- 


f 


i 


:i 


I 


111.  No.  15 
T 


m 


Lowell  Mason,  "  Hebron  " 
S  T  S         D         T 


^^ 


(IS 


-(=z- 


l=£ 


72 


CUMULATIVE    HARMONY 


These  exercises  should  be  transposed  to  various  minor  keys  and 
harmonized  in  accordance  with  given  directions. 

As  the  3d  from  the  fundamental  in  all  D  chords  is  required  to  be 
major,  and  as  that  note,  according  to  the  key  signature,  is  minor,  it 
must  necessarily  be  elevated  in  order  properly  to  form  such  chord. 

The  subtonic  thus  becomes  a  leading  tone  with  a  tendency  to  re- 
solve upward  to  the  Tonic. 

This  necessitates,  therefore,  the  elevation  of  the  seventh  degree  of 
the  scale  in  such  transposition. 

Exercise  167  transposed  to  a  would  appear  as  follows: 


169 


i 


-^ 


1^ 


r  r 


r  r 


r  r 


± 


s^ 


*   ft 


^ 


f 


-5 


«6 


S6 
4 


z^ \ i r    ^              -              1         I-— 1 -==q -r- 

^fej    ^    g^4=f — r^  ^    J  rJ  H    ^  ^ J    ^    J 

L- t^-Mf ^ — 1 ' *■ — ff ' Lfff m 1 

n                                                           1                     1      '             1 

-vT-^ 1 ] 1-      1      \ 1 ^-  ^ a ^ ^ \ 

C^  2_<5^ 0—i-^ S ^     1  (&'  •   1 — *    ff — lJ 1 1 ffr_J U 

CHAPTER   XIV 
HARMONIZATION  OF  MELODIES.     (Continued) 

Rule  V.  When  a  primary  note  or  fundamental  is  followed  by 
another  a  fourth  higher,  a  D^  chord  may  be  formed  upon  it,  effect- 
ing a  passing  modulation. 

This  frequently  occurs  when  the  T  chord  is  followed  by  the  S 
chord,  the  T  chord  becoming  a  passing  Dominant  to  the  key  of  the 
Subdominant  as  by  Rule  I  of  Serial  Modulations.  The  Tonic  chord 
thus  becomes  temporarily  a  Dominant  of  the  Subdominant  [DS]. 


170 


T  (a) 


(^) 


St 


is: 


(i; 


-z^ 


^ 


S^ 


b7 


At  (a)  is  the  usual  harmonization  of  the  first  of  the  scale  with  the 
Tonic,  and  repeated  with  the  Subdominant. 

At  (b)  the  minor  7th  Bb  is  added  to  form  a  D^  chord  and  a  passing 
modulation,  as  by  Rule  I  of  Serial  Modulations. 


m.  No.  le 


B^ 


Chwatal,  "  Lovely  Night " 


^ 


5 


^ 


-X ^ZL 


-<5*- 


r 


0^ 


i 


t±s. 


ife 


S^ 


m 


f 


•Passing  modulation  as  a  Dominant  of  the  Subdominant. 

The  following  exercise  involves  the  application  of  the  preceding 
five  rules,  and  should  be  worked  out  in  several  keys. 

73 


74 


CUMULATIVE   HARMONY 


171 


(a) 


{b) 


-z=*- 


-25^- 


-7^ 


I        I       I 


f- 


J£ 


4 


-^^ 


J-:^ 


J 


■'^      G 


^ ^ 


-(2- 


■^2 ^ 


hS^- 


5-b7 


b7 


i 


-f2- 


At  (a)  the  first  of  the  scale  is  harmonized  with  the  Tonic;  but,  as 
the  fundamental  C  moves  upward  a  fourth  to  F,  a  passing  modula- 
tion may  take  place  by  forming  a  D"  chord  on  the  primary  note  C. 

As  the  initial  chord  should  be  the  T  triad,  the  yth  is  added  only  in 
the  latter  half  of  the  chord,  thus  effectually  forming  from  the  Tonic 
a  passing  Dominant  of  the  Subdominant  [DS]. 

At  (&),  in  order  to  separate  the  upper  three  voices  more  equally, 
the  tone  common  to  the  two  chords  is  not  retained  in  the  same  voice; 
at  (c)  the  fifth  of  the  scale  is  harmonized  with  the  Dominant  to  con- 
form to  the  rule;  at  (e)  the  fourth,  followed  by  the  third  of  the  scale 
is  harmonized  with  the  Dominant;  and  at  (/)  the  D^  descends  to  the 

At  id)  the  primary  note  C  again  moves  upward  a  fourth,  inviting 
a  passing  modulation  to  the  Subdominant.  As  this  is  preceded  by 
the  D^  chord  on  the  note  G,  the  use  of  two  D^  chords  in  immediate 
succession  is  involved. 

This  may  occur  when  a  normal  D^  chord,  followed  by  its  T  chord, 
is  in  turn  succeeded  by  a  S  chord,  inviting  a  passing  modulation 
through  forming  a  seventh  chord  on  the  Tonic  and  making  that  note 
temporarily  a  Dominant. 

It  may  be  seen  in  the  above  example  that  the  D^  [B],  instead  of 
resolving  to  the  T^,  is  chromatically  altered  to  become  the  yth  in  the 
passing  Dominant  chord.  The  effect  of  this  is  as  though  the  3d  [B] 
had  resolved  to  the  8va  [C]  and  then  proceeded  to  the  Bb  to  aid  in 
forming  the  new  Dominant. 

Therefore,  when  a  D^  chord  is  followed  by  another  in  immediate 
succession,  the  3d  or  5th  need  not  be  omitted,  as  the  usual  resolution 


HARMONIZATION    OF    MELODIES 


75 


to  the  T  triad  is  not  affected.  The  3d  of  the  first  Dominant,  in- 
stead of  resolving  to  the  8va  of  the  Tonic,  is  chromatically  altered  to 
become  the  7th  in  the  succeeding  chord. 

The  student  is  cautioned  against  the  employment  of  a  note  in  one 
voice  part  immediately  followed  by  its  chromatic  alteration  in  an- 
other. 

This  leads  to  the  announcement  of  the  following  most  important 
principle  in  the  theory  of  music. 

As  a  chord  consisting  of  a  major  3d,  perfect  5th,  and  minor  7th,  or 
an  inversion  of  the  same,  is,  and  may  be  considered  only  as,  a  D^  chord 
whose  fundamental,  regardless  of  the  key  indication  of  the  signature, 
must  itself  be  a  Dominant,  it  is  obvious  that  wherever  it  appears  it 
clearly  identifies  an  individual  tonality,  whether  or  not  it  is  followed 
by  a  resolution  to  a  corresponding  Tonic  triad. 


in.  No.  17 


Chopin,  "  Mazurka  in  G  Minor,"  op.  67,  No.  2 


7  ?7 

A  A     A  A     A  A 

*  A  series  of  D^  chords  representing  the  following  keys:C  or  c,  F  or  f,  Bb  or  bb, 

A  A        AAA  AA  A  A  A 

Eb  or  eb,  Ab  or  ab,  Db  or  db,  Gb  or  gb  and  Cb  or  cb. 


172 

I 

1 

<i 

1 

1 

1         1 

1 

yKn     e^. — 

—^ h 

<>             ^ 

^ 7^ ^S) 

—rs — ^ — 

( 

CCDa        . — 

=5 f?       ^ 

-^ ^ 

— ^ —fit — 

\ 

1 

( 

Xi'^  ^- — 

1           1           ' 
J       -i      -J- 

1 
-G>-           -6>^ 

r   r   r 

etc. 

L^^SiLi 

— ^ 

^— 

^9,'^' 

hS2 ^a_ 

CL- 

--    (^—  \ — 

^-^ ^f \ T-" T-^ \ —^ ■ 

-j^-^ — ^    r^ 

^ (Si— 

-^ — (^ — f- — 

1 

-^ — «» — 75- 

'(])  ^'           ! 

-1 r        \— 

1 — 

1 \ f^ 

--^ ^2 ^ 

— 1 ' 1 

i\^ 1 ^ 

Jr    f» — Ki — ^— 

i'-'    ? 

z-^=i^ ^ 

— ' 1 "-V- 

1 1 ' 

'-^' — H 

B 

B>  1      ! 

f— 

— 

1 

— ^ 

h 

=j 

^ \ 

— — w 

76 


CUMULATIVE   HARMONY 


173 


i 


;i=f^ 


-(2Z (2- 


-(S G>- 


E^ 


<2 f5> 


r=^     r? 


-« — (ffi- 


5?^ 


i 


■«'— 7-*=^ f=^ 


-«^ f=2- 


-(2 «>• 


P 


-f2- 


-*2 «.- 


174 

--,1^-^ ^^9—^ ^ ^-{S- f^-^ ^-^ h— -^ 

:ig)(/  ^     1^    :^—       ij^" — '^-'^— 1^-:               H -| ^ — 

i 


fs — s-- 


<g^^ — r^     rs=-(g — (2^ 


-«> — f^ 


:^z=;^=:s 


P 


175 


-vVr-    r    r^    r   -f    r^    r    r   r-f— r^^^-^H 

-^>*^^-r ^-^-^ i^ ^ — -' — ' — ^ 1 

1 — 9-^ — «-— rP fg'    1  r^ "S-— r<S' ?5 ^; 1 ::r-T ^ n 

\A£-4^     1     |h     \-\\       f-   1^     r^     ^   Ip-     ^_^^^ 

Transpose  these  exercises  to  many  keys  and  harmonize  similarly. 

Transpose  to  minor  keys  and  harmonize  similarly.  As  the  T 
chord  in  the  minor  mode  is  a  minor  triad,  the  3d  must  be  elevated 
in  forming  a  DS  chord. 

176  (a) 


i 


w^- 


gte 


=# 


f- 


-fg — ::^ 


j- 


?:^«? 


-fg- 


:J-a 


^ 


etc. 


4 ^- 


5-      # 


At  (a)  the  second  quarter  appears  as  a  DS  chord,  the  T^  having  been 
elevated  as  required. 

Progressions  of  voice  parts  by  augmented  interval  should  generally 
be  avoided.  This  applies  particularly  to  augmented  2ds  and  4ths 
ascending.  Augmented  2ds  are,  however,  sometimes  unavoidable 
at  present  in  given  melodies  transposed  to  minor  keys. 


CHAPTER   XV 

HARMONIZATION  OF  MELODIES.     (Continued) 
Employing  Inversions 


The  following  exercises  should  be  harmonized  in  accordance  with 
the  preceding  rules,  the  student  employing  the  inversions  of  the 
various  chords  in  such  manner  as  to  form  diatonic  passages  of  greater 
or  less  length,  with  a  view  to  making  the  bass  part  as  melodious  as 
possible. 

These  exercises  should  be  worked  out  in  both  close  and  open  position. 

177 

(a)     (d)     (c)  id)     (e) 


m 


i 


3 


i 


f 


:it 


=3= 


-z^ 


z=^ 


6  6 

4        b5 


i 


-Z5>- 


-O- 


^ 


P. 


'S- 


f 


-^ 


-^ 


:^ 


r 


m 


f- 


r 


i 


J 


^    j  ,j 


53 


=^p: 


5 


5 


I^^ 


f 


3t 


-3-- 


V 


n 


3 


6 


4 

3 


^ 


6 
4 


-i5^ 
6 

77 


78 


CUMULATIVE   HARMONY 


At  (a)  the  seventh  of  the  scale  is  harmonized  with  the  Dominant, 
the  chord  consisting  of  G,  B,  D,  and  F.  In  selecting  from  these  a 
note  for  the  actual  bass,  care  must  be  taken  to  avoid  choosing  such 
one  as  would  occasion  faulty  doubling  with  the  given  melody  note; 
therefore  the  B  in  the  melody,  which  is  the  3d  from  the  fundamental, 
must  not  appear  in  the  bass.  By  selecting  F  a  diatonic  bass  passage 
of  several  notes  may  be  obtained.  As  F  is  the  7th  of  the  Dominant, 
it  must  be  followed  by  the  T^  for  resolution,  as  at  (b). 

At  (c) ,  as  the  fourth  of  the  scale  followed  by  the  third  receives  the 
D  harmonization,  and  as  D  is  one  of  the  available  notes  of  the  chord, 
it  is  selected  in  order  that  the  passage  may  be  continued  diatonically 
downward.  The  bass  passage  continues  in  the  next  chord,  where  the 
bass  note,  C,  being  the  resolution  of  the  D^,  is  one  degree  further  in 
the  same  direction. 

At  (d)  the  D^  is  not  available,  as  its  resolution  appears  in  the  soprano 
at  the  next  chord.  At  (e)  the  primary  note,  ascending  a  fourth,  in- 
vites a  passing  modulation  by  Rule  I. 

Exercises  173,  174,  and  175  should  be  worked  out  similarly  in 
many  keys. 

The  same  exercises  may  be  worked  out  in  quarter-note  motus, 
using  fundamental  positions  and  inversions  as  follows: 

178  ,111, 


T-Z^ 


r 


f 


6  4        2 

J  ^    I    J 


6        4        6 


etc. 


El 


IhE 


?"=S 


T 


r  f  V 


rr^r 


r 


Before  proceeding  further  with  this  section  of  the  work  special 
consideration  of  the  4  chord  is  necessary. 

This  chord,  which  is  the  second  inversion  of  the  triad,  is  a  peculiarly 
dependent  one,  and  is  seldom  used  with  good  effect  except  in  con- 
nection with  other  chords  upon  which  it  directly  depends  for  a  satis- 
factory existence. 

It  is  best  employed  with  the  following  conditions: 

I.  When  preceded  and  followed  by  a  triad  or  seventh  chord  upon 
the  same  bass. 


HARMONIZATION    OF   MELODIES 


79 


179 


(a) 


(^) 


« 


-&.- 


(m 


-&- 


At  (a)  the  4  chord  is  preceded  and  followed  by  the  triad  on  the 
same  bass  note,  C.  At  (b)  the  I  chord  is  preceded  by  a  triad  and 
followed  by  a  D^  chord  on  the  same  note,  G. 

II.  When  it  occurs  between  two  bass  notes  a  diatonic  degree  above 
and  below  its  bass. 


180 


(a) 


{^) 


i 


m 


m 


-j^ 


3s: 


At  (a)  the  4  chord  occurs  between  the  bass  notes  E  and  C.  At  (J) 
it  occurs  between  the  bass  notes  F  and  A.  In  both  instances  it  acts 
as  a  passing  chord  between  two  different  positions  of  another  chord. 

III.  When  it  is  preceded  or  followed  by  other  positions  of  the  same 
chord. 


181 

J    V 

/k       o> 

a 

— ^ 

r3 

\m — ^ 

^ 

— «> 

~f 

< 

1 

ej 

i^* 

^5 <& — 

1 ^fil — 

r"          J-J 

1 — 

J — ^ 1 

IV.  When  it  is  followed  by  a  triad  or  seventh  chord  on  the  same 
bass  for  the  formation  of  a  cadence  (to  be  considered  later),  or  when 
as  the  second  inversion  of  the  T  chord  it  is  followed  by  the  third  in- 
version (or  the  first  inversion)  of  a  D  chord. 


So 


CUMULATIVE   HARMONY 


182 


(a) 


^ 


(*) 


M 


(.<r> 


U) 


^ 


i 


i 


3 


-<^-^>9- 


-SkS'- 


-^      fS 


6       5 
4 


At  {a)  the  4  chord  is  followed  by  a  triad;  at  (6),  by  a  D^  chord,  both 
of  which  in  turn  are  followed  by  a  triad  on  the  Tonic.  At  (c)  the  \ 
chord  is  followed  by  the  third  inversion  of  the  D^  chord  on  G,  figured 
2,  which  is  resolved  to  the  first  inversion  of  the  Tonic,  C.  At  {d) 
and  {e)  it  is  followed,  respectively,  by  the  first  inversion  of  the  D'^ 
chord  and  of  the  D  triad. 

The  bass  in  this  chord  is  generally  doubled. 

The  initial,  final,  and  penultimate  notes  of  the  bass  part  should  be 
in  fundamental  position. 

The  S  chord  should  not,  for  the  present,  follow  the  D  chord. 

The  student  should  carefully  avoid  overlapping  the  voice  parts, 
particularly  the  bass,  which  must  not  appear  above  the  tenor. 


The  Abbreviated  D^  Chord  D) 

With  the  fundamental  omitted  from  the  D^  chord,  the  three  re- 
maining notes  present  a  series  of  thirds  forming  a  triad  on  the  sub- 
tonic,  as  a  leading  tone. 

The  subtonic  is  here  considered  its  nominal  fundamental,  its  real 
fundamental  being  the  Dominant.     Symbol,  D). 

This  chord  is  at  its  best  in  its  first  inversion  (D^  in  the  bass),  and 
with  the  D^  in  the  soprano;  it  is,  in  fact,  otherwise  not  very  satis- 
factory, and  is  rarely  employed. 

In  this  position  the  D^  is  doubled  when  the  chord  is  followed  by 
the  first  inversion  of  the  T  triad  [a) ;  when  it  is  followed  by  the  T  triad 
in  fundamental  position,  the  7th  is  doubled,  one  resolving  to  the  T^ 
and  the  other  ascending  to  the  T^  (Z»). 

The  second  inversion  (D^  in  the  bass)  is  acceptable  only  with  the 
D^  doubled   (c). 


HARMONIZATION   OF   MELODIES 

183 


8l 


(«) 


i 


i^^ 


w 


6) 


->»- 


1         J. 


(6) 


i 


zt 


^=f 


6) 


(0 


-fS*- 


-i 


■422- 


The  chord  is  rarely  used  in  its  fundamental  position,  and  the 
student  would  do  well  to  avoid  it. 

This  chord  was  much  fancied  by  the  old  masters,  who  generally 
omitted  the  fundamental  in  the  second  inversion  of  the  D^  chord. 


m.  No.  18 


t^A^ 


Haendel,  "  Belshazzar  " 


^^ 


^ 


s 


N 
-^ 


i-l^ 


i  1 


^a- 


E 


^        k 


Mozart,  "  Fantasia  in  C  Minor  " 


m.  No.  19 


m 


^  J  J  i  1 


S 


1^ 


x^ 


(^^f^ — f 


^ 


s 


-=^— »- 


6^6 


t(6) 


184 


(^ 


i 


^i=F4 


5 


3 


-5t- 


etc. 


pe 


^ 


3 


1 


2C 


-<»- 


f 


6)  6 

b5 


!) 


82 


CUMULATIVE    HARMONY 


r^i) 


6 
b5 


\>7 


ii6 

4 
3 


6) 


-^ |ii^ 


lfc-TT~~^f^ 


-f2- 


I 


185 


Eg 


S6) 


H=2- 


-zj^- 


6) 


^6) 


J 

, 

, 

J 

/^\»                 1                          1 

1                  1 

1          i                  1 

1         1 

l^y  • 

^ 

; 

1 

'V 

1 

^ 

\^-/          "-^                 ex 

1    z? 

si            '^            1 

III                        ^ 

1 

#6) 


6) 


-<^ 


6) 


S6) 


CHAPTER   XVI 
SECONDARY   CHORDS   ON  THE   SUBDOMINANT 

In  the  Subdominant  chord,  the  6th  may  be  substituted  for  the  5th, 
to  form  the  Subdominant  substituted  6th  chord.     Symbol,   [S. 

This  chord  is  an  application  of  the  triad  of  the  supertonic  (which 
is  its  fundamental)  to  Subdominant  harmonization,  and  will  be 
directly  considered  only  in  connection  with  and  as  a  member  of  the 
family  of  S  chords. 

It  has  the  greater  local  significance  as  a  primary  chord  when  it 
appears  in  its  primary  position  with  the  Subdominant  as  the  bass, 
although  in  both  its  fundamental  and  4  position  the  Subdominant 
character  is  always  present,  excepting  when  in  its  fundamental  position 
it  is  preceded  by  such  dissonant  chord  as  would  tend  to  localize  it  as 
a  point  of  destination  or  partial  repose.  As  in  the  triad,  it  is  the  S' 
that  is  not  suitable  for  doubling.  This  is  particularly  true,  as  to  its 
application,  in  the  major  mode.  It  may  be  understood  that  the 
minor  3d  from  the  fundamental  of  any  chord  is  not  as  objectionable 
for  doubling  as  is  the  major  3d. 

This  chord  may  be  freely  used  in  all  inversions,  as  exemplified  with 
symbolized  figuring  in  the  following: 


186 


{a)        {b) 


^ 


{c) 


id) 


{e) 


^ 


-7S>Kr 


P^^ 


i 


1 5  or  13 


^ 


At  (a)  is  the  triad  of  the  Subdominant,  F,  in  the  key  of  C.  At  {b) 
the  6th  is  substituted  for  the  5th.  At  (c),  (J),  and  {e)  are  given  the 
chord  m  its  various  positions,  with  symbolized  figuring. 

83 


84 


CUMULATIVE    HARMONY 


The  secondary  Subdominant  symbol  L  is  used  in  connection  with 
this  chord  for  purposes  of  immediate  identification,  and  as  an  aid  in 
subsequent  analysis. 


m.  No.  20 

Andante 


Beethoven,  "Sonata,"  op.  14,  No.  2 


-::ir ^ 


■A—*-       1    =^ 


in.  No.  21 


F.  GiARDiNi,  "  Italian  Hymn" 


^azzt 


^:i^ 


^ 


4: 


^=r 


£ 


6       lA       4 

In  the  Subdominant  chord  the  6th  may  be  added  to  the  triad  to 
form  the  Subdominant  added  6th  chord.      Symbol,    [[S. 

This  chord,  in  like  manner,  is  an  application  of  the  supertonic  7th 
chord  for  Subdominant  harmonization,  and  will  be  classed  directly 
as  another  member  of  the  family  of  S  chords. 

It  may  be  freely  used  in  all  positions,  the  figuring  for  which  should 
have  the  special  symbol  (  1J_)  attached. 


187 


i 


{a) 
-U 


(^)         {c)        {d)       {e)        (/) 


-si- 


"S: 


-^^ 


[w 


-^ 


'^L 


-Z5^ 


-^ 


111 


^ 


13 


A 

At  {a)  is  the  S  triad  in  the  key  of  C.  At  (6)  the  6  th  is  added  to 
the  triad.  At  (c),  ((/),  (e),  and  (/)  the  various  positions  of  the  chord, 
with  symbolized  figuring,  are  given. 


SECONDARY   CHORDS   ON    THE   SUBDOMINANT 


85 


m.  No.  22 


Mendelssohn,  "Part  Song" 


i?^^ 


^ 


i 


^ 


r 


4-^ 


m^ 


^^ 


IS 


e: 


5^ 


g± 


-fii!- 


116  U* 

Il5_ 

Although  the  fundamental  of  the  chords  of  the  substituted  and 
added  6th  on  the  Subdominant  is  the  supertonic,  the  Subdominant 
remains  the  primary  note  of  the  chord,  and  the  passing  modulation 
effected  by  one  primary  note  being  followed  by  another  a  fourth 
higher,  is,  therefore,  applicable;  this  occasions  one  form  of  what  is 
known  as  the  deceptive  cadence,  which  will  be  brought  more  ex- 
tensively to  notice  later  on. 

188 


i 


:^=m 


:^ 


m 


e)     r"- 


:|^ 


&)        eJ- 


£ 


^ 


~4^ 


-rJ         <^ 


6 
b5 


b7 


b7 


The  progression  of  the  various  notes  of  this  chord  is,  in  general,  to 
the  notes  lying  nearest  in  the  succeeding  chord,  but  in  such  manner 
that  no  faulty  parallel  5ths  or  8vs  appear.  The  probability  of  the 
occurrence  of  such  faulty  progressions  is,  in  this  connection,  yery 
great. 

When  the  fundamental  position  of  the  [jS^  chord  (expressed.  Sub- 
dominant  added  6th  chord)  is  followed  by  the  fundamental  position 
of  the  D  chord,  the  S^  may  be  omitted,  and  the  fundamental  (super- 
tonic)  doubled,  as  in  the  D^  chord. 

180 


i 


-TCi- 


-izt 


V. 


Lil 


M 


-6<- 


S6 


CUMULATIVE   HARMONY 


In  the  major  keys,  the  S^  may  be  depressed.     This  applies  to  the 
[S  and  the  [[S  chords  as  well  as  to  the  triad. 

190 


D 


D 


D 


is: 


-stg- 


±i: 


As  the  tendency  of  elevated  notes  is  to  progress  upward  and  of  de- 
pressed notes  downward,  the  depressed  3d  in  the  S  chord  should  pro- 
gress downward  one  degree,  rather  than  an  augmented  second  to 
the  degree  above,  when  the  S  chord  is  followed  by  the  D  chord. 

m.  No.  23  Chopin,  "  Nocturne,"  op.  32,  No.  i 


The  extension  of  the  list  of  S  chords  as  given  above  suggests  the 
following  additional  rule  for  harmonization. 

Rule  V.  The  second  of  the  scale  may,  at  times,  be  harmonized 
with  the  Subdominant. 

As  the  second  of  the  scale  is  the  S^,  it  is  obvious  that  only  the  [S 
and   [|S^ chords  may  be  employed  in  its  harmonization. 

191 


-I    -X 


-55*- 


J. 


-(^ 


^ 


f- 


1^ 


5   -   b7 


i5 


SECONDARY   CHORDS   ON    THE   SUBDOMINANT 


87 


At  (a)  the  second  of  the  scale  is  harmonized  with  the  Subdominant, 
using  the   [[S^ chord  in  primary  position. 

At  (b)  the  second  of  the  scale  is  harmonized  with  the  Subdominant, 
using  the  [S  chord  in  fundamental  position.  As  the  primary  note  is 
the  Subdominant,  F,  the  preceding  primary  note,  C,  being  followed 
by  another  a  fourth  higher,  is  converted  to  a  temporary  Dominant  by 
addition  of  the  7  th. 

The  simple  existence  of  the  D^  chord  on  C  involves  a  temporary 
modulation  to  the  Subdominant,  and  is  resolved  equally  well  to  all 
forms  of  the  S  chord. 


192 


(a)    id) 


(O 


^ 


=¥ 


J^E 


-i^^^^i 


-J- 


-:^ 


J 


(^)    (^) 


^^ 


i 


V    ^ 


A 


-25^ 


^ 


(/)  U) 


L5_       7 


6 

b5 


M 


? 


s 


r 


:«=S: 


Pi 


^^d-^ 


d?*: 


I|6 


-     7 


At  (a)  the  primary  note,  C,  being  followed  by  the  primary  note, 
F,  is  converted  into  a  temporary  Dominant  by  addition  of  the  7th, 
Bb.  At  (b)  the  depressed  3d  is  used  in  the  first  inversion  of  the  S 
triad.  At  (c)  the  second  of  the  scale  is  harmonized  with  the  [S 
chord  in  fundamental  position.  The  primary  note,  C,  at  (d)  is  con- 
verted to  a  temporary  Dominant  moving  to  the  primary  note,  F,  with 
the  [S  chord.  At  (/),  (g)  the  harmonization  of  the  second  of  the  scale 
is  divided  between  the  [|  S  and  the  D^  chords.  At  (h)  the  fourth  of 
the  scale  is  harmonized  with  the  Subdominant,  and  at  (i)  the  second 
of  the  scale  is  given  the  |]S^ chord  with  depressed  3d. 

The  following  examples  should  be  worked  out  with  application  of 
the  given  forms  of  the  S  chord,  alternately,  for  practice. 


si 


88 


CUMULATIVE    HARMONY 


193 

I* 

/ 

^ 

^ 

.^ 

y   />     o 

[ 

1*       1         1         r 

<r^                 .^^ 

\i     r 

1 

1 

1                            1 

r 

1 \ 

U 4- 1 

^ 


-^ — ^ 


I 


-^ — #- 


194 


!§= 


g 


^=F 


^=2- 


i 


1^ 


IE 


^ 


I 


Dominant  of  the  Dominant  [DD],  Passing  Modulation 

The  admission  of  the  [[S^  to  the  list  of  those  available  for  harmoni- 
zation invites  in  turn  a  second  application  of  the  rule  for  passing 
modulation  as  given  on  page  73. 

The  one  already  in  use  occurs  when  the  Tonic  as  a  primary  note  is 
followed  by  the  Subdominant  as  another  primary  note,  a  fourth 
higher. 

When  the  [[S^  chord,  whose  fundamental  is  the  supertonic,  is  fol- 
lowed by  a  D  chord,  the  fundamental  of  which  is  a  4th  higher,  a  D^ 
chord  may  be  formed  upon  it,  effecting  a  passing  modulation  as 
a  Dominant  of  the  Dominant  [DD]. 

As  the  given  melody  may  not  be  altered,  the  necessary  chromatic 
alteration  must  be  made  in  the  lower  voices. 

195 

(a)  {b)      {c)  (d) 

I  _l  1  I  I  I  I  1 


-1^ 


-(^- 


r 


.1 


m 


-<^ 


^^ 


-^2- 


6       6 
5       5 


\\1 


SECONDARY   CHORDS   ON    THE   SUBDOMINANT         89 


i 


i 


J- 


-rr 


J_A 


.1 


g 


i^  #     b# 


^^ 


ipzzip: 


r^ 


fe 


i  -i  ^ 


J 


E^^ 


E 


r 


6 
b5 


I A    I 


112 


i 


(') 


J_J 


^ 


-25*- 


:^ 


f^^ 


ii: 


-i 


^ 


J 


■^- 


=^ 


-(5i^ 


31 


r 


#6 
4  4 
3     3 


\1 


6 
1^5 


|5 


At  (a),  in  order  to  prevent  the  soprano  and  alto  from  being  too  far 
apart,  the  inner  voices  have  been  exchanged.  At  {h)  the  second  of 
the  scale,  harmonized  with  the  [S  chord,  is  followed,  at  (c),  by  the 
third  inversion  of  the  D^  chord,  F  serving  as  the  bass  in  both  chords. 
At  {6)  the  first  of  the  scale,  C,  repeated,  receives  the  ||S  harmonization, 
with  a  supertonic  fundamental,  which,  being  followed  by  a  funda- 
mental (G)  a  fourth  higher,  is  altered  to  become  a  D^  chord  [DD]; 
this  has  been  done  in  the  last  half  of  the  note,  thus  effecting  a  passing 
modulation  (as  DD)  agreeing  with  Rule  II  of  the  Serial  Modula- 
tions. 

A  similar  case  is  at  (g),  where  the  chromatically  altered  note  ap>- 
pears  in  the  alto.  This  may  be  accomplished  also  by  chromatically 
altering  the  3d  (F)  immediately  upon  reaching  the  fundamental 
located  a  fourth  higher,  leaving  the  [jS  form  of  the  chord  to  be  implied; 
but  the  student  is  advised  to  do  so  but  rarely,  until  its  meaning  is 
thoroughly  absorbed,  in  order  that  the  original  idea  in  the  harmoni- 
zation should  not  be  lost. 


90 


CUMULATIVE   HARMONY 


196 


{a) 


ib) 


{c)     {d) 


-f^- 


-^5*- 


-^- 


4 


:i 


f=«f=P^ 


^ 


5    - 


If6 


At  (a)  the  first  inversion  of  the  D^  chord  is  resolved  to  the  T  triad, 
upon  the  last  half  of  which  at  {h)  a  DS  chord  is  formed  leading  to  the 
[jS  chord;  this  in  turn  is  altered  at  (c)  to  become  a  DD  chord  suc- 
ceeded at  {d)  by  the  triad  and  yth  chord  on  the  normal  Dominant. 

In  the  following  example  the  same  harmonizations  are  given  with 
the  intermediate  normal  progressions  omitted,  although  implied, 
and  the  passing  modulatory  progressions  approached  directly. 


197 


DS 


DD 


m 


-s*,- 


-s^- 


-^ 

# 


-Tzi- 


\' 


As  will  be  seen  from  the  above,  D^  chords  may  follow  one  another 
in  immediate  succession,  thus  effecting  a  series  of  passing  modulations 
by  successive  D  chords. 

m.  No.  24  Chopin,  "  Waltz  in  C#  Minor, "  op.  64,  No.  2 


■y. 


s^te 


mf 


£ 


IS 


7 

#5 

X 


*The  D^  chord  on  D#  followed  by  the  D^  chord  on  G#. 


SECONDARY   CHORDS   ON    THE   SUBDOMINANT         91 
lU.  No.  25  Mendelssohn,  "  St.  Paul " 


i 


E 


W^ 


3: 


w 


-^^-■ 


1=F- 


J: 


S?J 


'  «6) 


r^^z 


*The  D^  chord  on  A,  followed  by  the  D  chord  on  D,  with  an  interpolated  % 
chord. 


The  application  of  D^  chords  in  this  manner  may  be  regarded  in 
general  as  an  effort  toward  intensifying  the  harmonic  progression 
toward  the  cadential  Dominant,  which,  with  its  resolution,  is  the  real 
point  of  destination. 

This  intensification  is  enlisted  primarily  by  the  substitution  of  dis- 
sonant chords,  as  chords  of  motion,  for  those  of  resolution  which 
create  an  impression  of  partial  or  complete  repose,  thus  deferring  the 
effect  of  finality  until  the  concluding  Tonic  harmony  through  its 
Dominant  has  been  reached. 

Work  out  the  following  exercises  in  both  major  and  transposed 
minor  keys,  introducing  passing  modulations  through  the  DS  and  DD 
chords,  opportunities  for  which  occur  with  the  following  harmonic 
successions:  T  to  S  chord  and   [[S^to  D  chord. 


198 

0 

m 

/ 

•  r 

(^      m 

> 

n 

Ki 

^^ 

ft/ 

/rs 

l<5 

t        1 

f? 

^J 

(^      r3 

ri 

(( 

\ry 

r 

; 

' 

1        1 

1        1 

%M 

1 

1 

1 

1         1 

1        t 

*. 

) 

' 

' 

' 

' 

1 

« 


-^ — (2- 


feE 


^ ^9 


-a      (g 


eJ     ^ 


I 


199 


i 


^  0 


i 


92/ 


CUMULATIVE    HARMONY 


i 


^ 


m 


i 


I 


¥ 


-^ ^ 


-^2_ 


200 


^ 


d        • 


^^ 


^       # 


-* — y- 


4=f= 


CHAPTER  XVII 


MELODIC  MODULATION 

We  have  learned  from  a  previous  chapter  that  modulation  is  effected 
melodically  by  establishing  a  correct  diatonic  scale  series  based  upon 
a  Tonic  other  than  the  prevailing  one. 

It  is  not  necessary,  however,  that  a  complete  new  scale  series 
should  appear  in  order  to  bring  about  such  modulation.  A  section 
of  one  key,  consisting,  possibly,  of  no  more  than  two  or  three  notes, 
may  be  assumed  to  be  in  a  foreign  key,  and  when  harmonized  ac- 
cordingly may  be  positively  identified  as  belonging  to  that  tonality. 


201    (a) 


J- 


ib) 


ic) 


=^ 


-75^ 


J    J 


A 


^ 


t^ 


^ 


-4^ 


-&- 


6 
b5 


I 

#6 
4 
3 


(^) 


Ke) 


% 


^ 


-X 


u 


t 


J. 


-(^ 


b7 


i?6 
4 
3 


At  (a)  we  may  assume  that  the  two  notes  G  and  F  (which  are  the 

A 

fifth  and  fourth  of  the  scale  in  the  key  of  C)  are  the  second  and  first 

A 

of  the  scale  in  the  key  of  F,  and  by  harmonizing  them  accordingly, 
they  become  positively  identified  with  that  tonality. 

93 


94 


CUMULATIVE   HARMONY 


At  (b)  the  D  may  be  assumed  to  be  the  fifth  of  the  scale  in  the  key 
of  G,  which  becomes  positive  by  harmonizing  it  accordingly.  At 
(c)  the  C  and  B  may  be  assumed  to  be  the  fourth  of  the  scale  fol- 

A 

lowed  by  the  third  in  the  key  of  G.     At  (d)  the  depressed  B,  which 

A 

is  not  a  part  of  the  diatonic  scale  of  C,  may  be  readily  assumed  to  be 

A 

the  fourth  of  the  scale  in  the  key  of  F,  and  at  (e)  the  elevated  F  may 

A 

be  taken  as  the  seventh  of  the  scale  in  the  key  of  G.  All  of  which  is 
substantiated  by  corresponding  harmonizations. 

Here  follows  a  series  of  rules  for  melodic  modulation,  at  indicated 
notes,  to  directly  related  keys.  As  modulation  is  effected  harmoni- 
cally through  the  Dominant  of  the  new  key,  the  indicated  notes  must 
necessarily  receive  Dominant  harmonization.  In  each  modulation 
the  new  key  will  be  retained  until  the  next  indicated  note  is 
reached. 

Rule  I.  When  the  indicated  (+)  note  of  modulation  descends, a 
half  step,  it  goes  to  the  third  of  the  scale  in  the  new  key. 


202 


J^a 


4- 


J- 


-TS)- 


^ 


-<2- 


1=^ 

(a) 


s^ 


^ 


-J. 


J 


J'  ^2_ 


?3? 


^-(3- 


-f^ 


b7 


\ 


At  (a)  the  indicated  note  of  modulation,  C,  descends  a  half  step 

A 

to  B,  which  becomes  the  third  of  the  scale  in  the  key  of  G,  and  as  C 
is  the  fourth  of  the  scale  followed  by  the  third,  it  is  harmonized  with 

the  Dominant. 

'^  .  .  . 

The  key  of  G  is  retained  until  we  reach  the  next  indicated  note  of 

modulation,  F,  which  descends  to  the  third  of  the  scale  in  the  key  of 

A 

C.     The  note  of   modulation  Bb  descends  to  the  third  in  the  key 

A 

of  F,  and  finally  the  note  F  descends  to  E,  the  third  in  the  initial 

A 

key  of  C. 


MELODIC    MODULATION 
111.  No.  26  Portuguese  Hymn 


mEMi 


# 


MM 


S 


^^ 


i 


it* 


fe^ 


i 


9S 


Rule  II.  When  the  indicated  (+)  note  of  modulation  ascends  a 
half  step,  it  may  go  to  the  first  of  the  scale  in  a  new  major  key,  or 
to  the  first  or  third  of  the  scale  in  a  new  minor  key. 


203 


(«) 


(^1 


.(^) 


y) 


(^) 


(/) 


U) 


^ 


-a- 


-fz- 


-B*- 


#? 


I 


(li 


ia 


^ 


Ai 


J- 


:ita: 


is: 


6      #4 
2 


^6 
4 
3 


At  (a)  the  note  of  modulation,  E,  ascends  a  half  step  to  the  first 
of  the  new  scale,  F.  As  the  E  is  the  seventh  of  the  scale  in  the  key 
of  F,  it  is  harmonized  with  the  Dominant,  C,  thus  definitely  eflfecting 
a  modulation  to  that  tonality. 

At  (b)  the  E  again  moves  upward  to  F,  but,  as  the  key  of  F  is  already 
in  force,  a  modulation  cannot  be  made  to  that  key;  therefore  the  E 

A 

moves  to  the  third  of  the  scale  in  the  key  of  d. 

Since  the  T^  occurs  in  the  soprano,  the  7th  may  not  appear  in  the 
preceding  D  chord,  as  its  use  would  cause  a  faulty  doubling  in  the  res- 
olution. 

In  the  second  measure  a  chord  with  C  in  the  tenor  is  succeeded  by 
one  with  C^  in  the  bass,  which  is  the  employment  of  a  note  in  one 
voice  part,  immediately  followed  by  its  chromatic  alteration  in 
another.  This  is  known  as  a  false  relation,  which,  while  usually  for- 
bidden, is  allowed  when  the  fundamentals  of  the  two  chords  involved 
are  a  3d  apart.  As  F  and  A,  the  fundamentals  of  these  chords, 
fulfill  these  requirements,  the  objection  does  not  apply. 


96 


CUMULATIVE   HARMONY 


At  (c)  the  indicated  note,  F#,  ascends  a  half  step  to  G.    As  G  is 
not  directly  related  to  F,  the  modulation  would  be  to  g,  which  being 

A 

represented  by  one  flat  more  than  the  key  of  F,  is  a  directly  related 
key. 

At  (d)  the  F#  again  ascends  a  half  step  to  G  and  may  invite  a  modu- 

A 

lation  only  to  the  tonic  major  key  of  G.  At  (e)  the  modulation  back 
to  C  is  obvious.  At  (/)  the  note  of  modulation,  C#,  ascends  to  D. 
As  the  key  of  D  is  not  directly  related  to  the  key  of  C,  the  modula- 

A 

tion  must  be  to  d.     At  (g)  the  modulation  returns  to  the  initial  key 


A 

of  C. 


m.  No.  27 


Michael  Praetorius,  i6io,  "Choral" 


E 


-^ 


m 


:^ 


£ 


^ 


t. 


W- 


ii 


:g: 


An  exercise  is  here  given,  involving  the  application  of  Rules  I  and 
II,  which  should  be  transposed  to  several  initial  keys  and  worked  out 
as  before. 

204 


^ 


p 


g*E 


^^ 


(i^-«2.-^ 


i 


42- 


fefefe 


'%p—~-f—%^- 


+ 


Rule  III.  When  the  indicated  (+)  note  of  modulation  descends 
a  whole  step,  it  goes  to  the  first  of  the  scale  in  a  major  key,  or  to  the 
first  or  third  of  the  scale  in  a  minor  key. 


MELODIC    MODULATION 


97 


At  (a)  the  note  of  modulation  descends  a  step  to  the  first  of  the 
scale,  F,  in  the  new  key.  G,  being  the  second  of  the  scale  in  the 
key  of  F,  is  harmonized  with  the  Dominant  of  that  key.     At  (b)  the 

A 

indicated  note  descends  to  D.     As  the  key  of  D  is  not  directly  re- 

A  ^  ^  A 

la  ted  to  F,  the  modulation  is  to  d;  at  (c),  a  modulation  in  the  same 

A 

manner  to  C.     At  (d)  the  same  succession  of  notes  involves  a  modu- 
lation to  a;  at  (e),  in  like  manner,  a  modulation  to  the  directly  re- 

A  A  A 

lated  key  of  d;   at  (/)  to  F,  and  at  (g)  the  return  to  C. 


m.  No.  28 


A.  F.  LwoFF,  1833,  "  Choral" 


^m 


:^=at: 


S 


4r-^Wr 


\^i4 


i 


'M 


|f6 
5 


Rule  IV.    When  the  indicated  (+)  note  of  modulation  ascends  a 
step,  it  goes  to  the  third  of  the  scale  in  the  new  key. 

206 


m 


-25*- 


321 


(Sf      <9- 


-f^ 


-.z^t 


mi 


■(^ 


m^ 


J: 


J 


-i 


-i  J 


J 


^^ 


E 


6      I 
4       7 


It  will  be  noticed  that  the  modulations  by  this  rule  are  effected 
without  the  use  of  the  7th  in  the  D  chord,  the  resolution  of  which 
would  cause  a  doubling  of  the  3d  in  the  succeeding  T  chord. 


III.  No.  29 


m 


Ahle,  1664,  "  Choral  " 


r 


g!Bi 


-3^ 

T 
I 


3 


«6 

4 


-J5'- 

T 


T 


98 


CUMULATIVE   HARMONY 


The  student  will  work  out  the  following  examples  after  Rules  III 
and  IV  from  several  initial  keys. 


207 


3 


* 


J^^EEE^ 


^ i^ 


(^ G> f9 1^ 


^^ 


-(2 (2 ^ 


-^ «? 


-fg gy 


208 


^ 


#: 


^ ^ f2 >9 


^ 


-fZ s> 


-(^ ^- 


fe 


^ 


I 


-(^ ^ 


^ (2 (Z ^ 


-^ Z? 


E 


-«2- 


RuLE  V.   When  the  indicated  (+)  note  of  modulation  is  repeated, 
it  becomes  the  fifth  of  the  scale  in  the  new  key. 


209 


-z^ 


■*-|        I 


J 


^ 


e 


T     g?        gl S^ 


?^ 


-(^ 


■¥ 


'^^ 


_i^_ 


f- 


ge 


J- 


-si- 


J-.i 


-g^    /=; 


-i 


-^-^ 


^ffi ^ — <9 


-f9 f2- 


-^2 ^- 


-r 

IJl       6 


6        4 


S4 


The  application  of  Rule  V  will  be  readily  understood  by  the  student 
without  special  comment. 

lU.  No.  30  Schumann,  "  Nachtstuck" 


E 


I 


-=J— 4- 


:^== 


'X^ 


±z^ 


K 


T^ 


^ 


MELODIC    MODULATION 


99 


The  following  examples,  including  the  application  of  all  the  five 
rules  for  modulation,  should  be  worked  out  from  various  initial  keys. 

210 


i^ 


^ 


-r>'~fg" 


:p:^=l:f 


i 


-^2- 


?^ 


-^— -(St 


.^g       -g). 


^^^ 


-(2 «2 


211 


f^=^ 


:fe=^=ifc=p^ 


=??^ 


-« — fi- 


-<2_ 


S=-^ 


f^—bo     >g=-& 


.#^^^4^ 


-<5! (2 (Si 


5^ 


■^ '9- 


Rule  VL  When  the  indicated  (+)  note  of  modulation  ascends  a 
fourth  or  descends  a  fifth,  it  goes  to  the  first  of  the  scale  in  the  new 
key. 

+ 

I 


212 


i 


-i- 


4 


-K>- 


r^ 


w 


:^- 


-s®- 


-5£: 


r 


% 


^ 


^ 


«6 

2 

+ 


«6 

4 

2 

+ 
I 


te 


-X 


^^ 


"If" 


:^ 


-f — r — 


-^ 


^^ 


-^ 


^ 


T 


$ 


#6 

«6 

if4 

6 

^6 

6 

#4 

l( 

2 

4 

5 

S2 

3 

*: 


+ 


-«'— — ^ 


g 


ICX3 


CUMULATIVE   HARMONY 


111.  No.  31 


i 


Neander,  1680,  "  Choral  " 

*         ^ 


-75J- 


•<&-       -z^ 


■p 


•^ 


J 


^- 


-1=2- 


Work  out  the  following  exercises  for  application  of  the  six  rules, 
from  various  initial  keys. 


213 


i 


B=?=f= 


^ — f^- 


-^ (S2- 


I 


^=-r9- 


-4S^ 


214 


+  + 


?^-^^-^^-^-'^r^"if~¥ 


lit 


^=r 


fe 


-(=2- 


fi 


g 


L  +  +  ^  +  +1 


+1         + 


I 


^ 


-.5^ ^ 


^^=^^-<^ 


Two  examples  follow  in  which  the  student  will  be  expected  to 
select  and  indicate  suitable  notes  of  modulation,  endeavoring  to 
apply  all  of  the  six  rules.  Care  should  be  taken  toward  effecting 
modulations  only ,  to  directly  related  keys.  The  instructor  may 
utilize  the  preceding  examples  with  the  indicatory  symbols  eliminated 
for  the  same  purpose. 


215 


S 

i 


m=F 


-(g-fe.g — f^MIr^^ 


-ig      <y    I  <?     1^   I  g     f^~\<9 


-v-^^v- 


->9 «> «- 


*^g=^*: 


i <^ 


-f^—W- 


^ 


P=f=^ 


I 


MELODIC   MODULATION 


lOI 


216 


i^xJxl^jX--^  r  ir  rir  r4f^^ 


^^ 


I 


-s^ 


^ 


■^ 19        <g 


:^ 


^ 


■^2 (5^ 


1= 


^  ^^ 

Double  indications  (-j-  +)  will  be  in  frequent  use  in  this  work. 
The  second  symbol  determines  the  modulation,  which  goes  into  effect 
at  the  first. 

217 


i 


-z^ 


W 


r 


r 


-^^ 


-j^ 


J- 


-^^ 


III 


m.  No.  32 


Barnby,  "  Bethlehem  " 


^i^ 


j^nm 


:#: 


&I 


3 


ff 


r 


^-m 


te 


^.^^ 


* 


3*=* 


'\i^^^'m 


w=^ 


til        6^  7  = 

4  m 


Additional  examples  follow: 

218 


?^=*-^>-^-^=F^^ 


£ 


7-^ 


:^=^ 


I 


m 


^ 


P 


-^=^W: 


^ 


102 
219 


CUMULATIVE  HARMONY 


T^^^^=r=r=^^  r  r  r 


'^—0- 


-F-^^ 


^f^ 


i^ 


\^=dt 


^h^=^ 


i^—i^ 


I 


220 


^_9_ ^i —  ^ ^ rr  ^ i^ ^ i;  1  ^. — if  -r-  f  n 

-jf'-i^- — irn* — T — f — ^'O — ^ — r^fTif  i      -» ^ .*"~ 

4>4-r — ^r-r-^' — ^ — ^^^ — i— LU  — ^- — 

u  +  +  +  +  +  ^^  +         + 


E=^^gE^S^ 


IS? 


221 


+     _   +       _  .       -t  ,  + 


^fe^sSi^^g^^^^^ 


^e^P^^r^ 


r^  •  1*-^ 


Ep 


T=tt 


A  A         .         A        A 


In  example  218  the  following  modulations  occur:  C  to  G,  e,  D,  d, 

A      ^  A 

F,  a,  and  C. 


CHAPTER  XVIII 
EMBELLISHMENTS 

An  embellishment  is  a  note  used  in  connection  with  a  chord  of 
which  it  does  not  form  a  part.  (It  may  also  be  a  deviation  from  a 
given  melody.)  The  list  of  embellishments  includes:  suspensions, 
retardations,  passing  notes  and  auxiliaries  of  various  species,  arpeggios, 
etc.,  which  will  be  marked  for  identification  by  the  diagonal  stroke 
through  the  body  of  the  note.     Symbol,  J   J    ^. 


Suspensions 

A  suspension  is  a  note,  which,  having  occurred  as  a  note  of  harmony 
in  one  chord,  is  sustained  or  repeated  in  the  same  voice  through  a 
portion  of  the  time  of  the  succeeding  chord,  of  which  it  does  not 
form  a  part. 

222 


i 


-i-F- 


<^  («) 


P 


-J- 


i 


(</) 


r 


■T — 

A  suspension  is  said  to  be  prepared  when  it  occurs  as  a  member 
of  the  chord  of  preparation,  as  at  {a) ;  suspended  when  it  is  sustained 
as  a  dissonance  in  the  succeeding  chord,  as  at  (6) ;  and  resolved  when 
it  descends  one  degree  to  a  harmony  note  in  the  same  chord,  as  at 
(c).  At  id)  is  given  the  two  chords  as  they  appear  without  the  sus- 
pension. 

The  classification  figures  8-4-3,  that  is,  preparation  8,  suspension 
4,  resolution  3,  indicate  a  suspension  of  the  fourth,  prepared  by  the 
octave,  and  resolved  to  the  third. 

103 


I04 


CUMULATIVE    HARMONY 


Such  classification  figures,  representing  the  preparation,  suspension, 
and  resolution,  placed  above  the  notes  so  represented,  may  be  used 
with  excellent  results  to  impress  upon  the  mind  the  functions  of 
the  various  notes  and  to  serve  as  a  medium  of  identification  and 
reference. 

In  the  classification  of  suspensions  it  must  be  understood  that 
the  various  species  are  distinguished  by  the  interval  distances  of 
the  various  notes  involved  from  the  primary  note,  and  not  from  the 
actual  bass  notes  as  in  the  case  of  symbolized  figuring. 

223 


f 


(a) 

I 


-fz- 


A 


^ 


ib) 


(O 


At  (a)  the  classification  figures  3-6-5  indicate  that  the  preparation 
E  is  a  3d  from  the  primary  note  C,  and  that  the  suspension  is  a  6th, 
and  the  resolution  a  5  th,  from  the  primary  note  G. 

At  {h)  the  preparation  is  a  5  th  from  the  primary  note  G,  the  sus- 
pension is  a  9th,  and  the  resolution  an  8va,  from  the  primary  note 
C.     Classification  figures  5-9-8. 

At  (c)  the  preparation  is  a  7th  from  the  primary  note  G,  and  the 
suspension  and  resolution  a  4th  and  3d  from  the  primary  note  C. 
Classification  figures  7-4-3. 

This  mode  of  classification  may  be  used  for  some  time  to  good  ad- 
vantage as  an  aid  in  impressing  on  the  mind  of  the  student  the  plan 
of  the  various  elements  of  the  suspension. 


224 


-4 — 3 


^^ 


s^S 


-z^- 


-H J- 


Ih 


(b) 


T 


I 


r 
4 


(o 


=^T 


EMBELLISHMENTS 


105 


Suspensions  generally  occur  on  the  accented  part  of  a  bar  (b)  or 
the  stronger  part  of  a  beat  (/). 

While  the  preparation  of  a  suspension  usually  occurs  on  the  un- 
accented part  of  the  bar  (a),  it  may  also  appear  on  the  accented 
part  (c),  and  when  tied  over  to  the  suspension  should  be  of  at  least 
equal  duration;  when  it  is  not  tied  to  the  note  of  suspension,  it  may 
be  shorter  (d). 

The  resolution  of  a  suspension  should  occur  on  the  unaccented 
part  of  the  bar  (e),  or  the  weaker  part  of  a  beat  (g). 

Progressions  that  are  faulty  without  suspensions  are  equally  or 
more  so  when  suspensions  are  employed. 

The  resolution  of  a  suspension  should  not  be  heard  in  another  part 
simultaneously  with  the  suspension,  excepting  in  the  bass  and  at  a 
distance  of  not  less  than  an  octave.  When  the  suspension  occurs  in 
the  bass,  the  resolution  should  not  be  heard  in  any  upper  part  except 
when  it  is  the  primary  note,  or  fundamental,  approached  by  degree  in 
contrary  motion;  in  such  circumstances,  the  simultaneous  employ- 
ment of  the  resolution  is  allowed  at  a  distance  of  a  seventh  or  more 
above  the  suspended  note. 

Note.  For  the  present,  at  least,  the  student  is  advised  against  doubling  the 
resolution  of  a  suspension  in  any  case,  except  when  it  is  the  primary  note,  or 
fundamental. 

With  the  figured  bass,  the  symbol  for  suspensions  is  the  radical  i^ 
placed  before,  and  inclined  downward  toward,  the  figure  representing 
the  note  of  resolution,  and  indicates  that  the  note  on  the  degree  above 
it  has  been  suspended. 

225 


i 


m 


f 
(.'-) 

^ 


f- 

K3 


r 


^ 


(O 


N6 
4 


At  (a)  the  symbolized  figure  N3  represents  the  triad  with  the  note 
above  the  3d  suspended  (C  suspended  above  B).  At  (b)  the  sym- 
bolized figures  represent  a  chord  of  ^^  4 ,  with  the  note  above  the  6th 
suspended  (C  suspended  above  B). 


io6 


CUMULATIVE    HARMONY 


When  the  suspension  occurs  in  the  bass,  the  figure  with  symbol 
representing  the  suspension  and  resolution,  thus,  r\i,  is  abbreviated 
to  the  symbol  alone,  n,  which  is  understood  to  mean  that  the 
actual  bass  forms  the  resolution  of  a  suspension  from  the  degree 
above,  as  at  (c). 

Note.  This  system  of  bass  figuring  with  suspensions  is  submitted  by  the 
author  to  satisfy  demands  that  may  be  advanced  for  general  systemization  of 
bass  figuration ;  but,  while  he  is  satisfied  that  it  is  the  simplest  as  well  as  the  most 
comprehensive  that  has  thus  far  been  offered,  he  would  advise  instructors  that 
satisfactory  results,  both  for  clarity  in  comprehension  and  for  subsequent  analysis, 
may  be  obtained  through  the  employment  of  the  classification  figures  above  the 
staff  and  without  the  use  necessarily  of  the  symbolized  bass  figuring. 

Rule  I.  When  a  primary  note  is  followed  by  another  a  fourth 
higher,  we  may  suspend  the  9th,  prepared  by  the  5th  and  resolved  to 
the  8va. 


The  primary  note  G  is  followed  at  (a)  by  the  primary  note  C, 
which  is  a  fourth  higher,  granting  a  suspension  of  the  9th  prepared 
by  the  5th  and  resolved  to  the  8va.  This  is  illustrated  by  the  classi- 
fication figures  5-9-8,  indicating  a  suspension  of  the  9th  prepared  by 
the  5  th  and  resolved  to  the  8va;  the  notes  and  the  symbolized  figuring 
i\8  indicating  a  suspension  of  the  note  above;  that  is,  the  9th,  D,  re- 
solved to  the  8va,  C. 

At  (b)  the  primary  note  C  is  followed  a  fourth  higher  by  the  primary 
note  F,  with  a  suspension  of  the  9th,  prepared  by  the  5th  and  resolved 
to  the  8va,  occurring  in  the  alto.  At  (c)  is  an  example  of  the  same 
suspension,  with  the  chord  of  preparation  in  the  second  inversion  and 
the  chord  of  suspension  and  resolution  in  the  first  inversion.  At  (d) 
the  chord  of  suspension  and  resolution  appears,  in  the  second  inver- 
sion. At  (e)  the  suspension  occurs  in  the  bass  with  the  symbolized 
figuring  as  described  above. 


EMBELLISHMENTS 


107 


The  symbolized  figuring  will  be  readily  understood  by  the  student 
without  further  comment. 


m.  No.  33 


^ 


Arthur  Sullivan 

"  St.  Edmund  " 
5 ^9 8 


^ 


=4: 


^'M 


r 

J- 


s 


-f^ 


r  r 


^ 


-f2- 


I\6 
4 


Rule  II.  When  a  primary  note  is  followed  by  another  a  fifth 
higher,  we  may  suspend  the  4th,  prepared  by  the  8va  and  resolved  to 
the  3d. 


227 


i 


-s>- 


-ir^ 


-J^ 


^ 


r 


4=^- 


r 


f- 


2-^5^ 


-;5*- 


(^) 


(^) 


-5^- 


(^0 


A 


^ 


^ 


■^-- 


p 


N3 


r 


N3 


K6 
4 
3 


6 

K 


At  (a)  the  primary  note  is  followed  by  another  primary  note  a 
fifth  higher,  inviting  the  suspension  of  the  4th,  prepared  by  the  8va 
and  resolved  to  the  3d.  At  {b)  the  primary  note  is  followed  by 
another  a  fifth  higher,  with  the  suspension  of  the  4th  in  the  alto.  At 
(c)  is  shown  the  same  suspension  with  the  second  inversion  of  the 
chord  and  the  attendant  figuring.  At  {d)  the  suspension  appears  in 
the  bass. 

The  following  exercises  should  be  worked  out  employing  the  sus- 
pensions admitted  by  Rules  I  and  II,  transposed  to  other  keys  for 
similar  working  out. 


io8 


CUMULATIVE    HARMONY 


228 


-4 3 

5 9 8  5- 


9 8         +5 9 8 

^ ^M—J- 


A 


"i—gi    >- 


-z^ 


■rT" 


■f- 


m 


sy 


4 


-si- 


-i 


etc 


sir 


^ 


.U-^- 


?^ 


-<S^ 


6 

K4 

2 


K6 


K6 


-^ 


-f2- 


-<2^ G> (2 ,a 


229 


a 


^ 19 G> fS*- 


-fS^ i9- 


^2 (S2- 


-f2- 


-^^ Z=^ 


4  11    ir 


^(=^— i:^ 


1^ 


5 


I 


f^—  -f9 f9 <9- 


111.  No.  34 


JOH.  Crueger,  1656,  "Choral" 
8 4 3  ^ 


z!E 


:^^ 


-s^ 


-^ 


r 


r^T 


-c*- 


J 


-f2 ^- 


111.  No.  35 


s 


'  K3 

Beethoven 

"  Symphony  II  "  op.  36 
4 3 


^^ 


J: 


F*=r: 


^ 


Zx|g- 


EMBELLISHMENTS 


109 


Rule  III.  When  a  primary  note  is  followed  by  another  a  fourth 
higher,  we  may  suspend  the  4th,  prepared  by  the  7th  and  resolved 
to  the  3d. 


230 


J: 


r^r  r" 


m 


J  ''U 


(O 


I^ 


A 


j'^U 


^ 


K3 


t\6 
4 


K3 


6 


At  (a)  the  7th,  F,  as  a  note  of  preparation,  is  suspended  in  the  fol- 
lowing chord  as  the  4th,  resolving  to  the  3d  in  the  same  chord.  At 
(b)  the  chord  of  suspension  and  resolution  is  in  the  second  inversion. 
At  (c)  the  chord  of  preparation  is  in  the  first  inversion.  At  (d) 
the  suspension  is  in  the  bass. 


ni.  No.  36 


Arthur  Sullivan,  "The  Lost  Chord' 
7 4 3 


IE 


^^w 


N3 


-^^v. 


K3 


CHAPTER   XrX 


SUSPENSIONS.     (Continued) 

Rule  IV.  When  a  primary  note  is  followed  by  another  a  fifth 
higher,  we  may  suspend  the  6th,  prepared  by  the  3d  and  resolved 
to  the  5  th. 

231 


-6 — 5 


-6 — 5 


-6 — 5 


-6-5 


i 


at 


-^ 


-s*- 


-7b- 


r 


-9      o 


M 


{d) 


{e) 


-^ — g^- 


-^:^^. 


-(2- 


-(^ 


^M=^ 


-(2- 


K5 


6  N6 

4  4 

2 


6 

K3 


I\5 


At  (a)  the  primary  note  C  is  followed  by  another  a  fifth  higher, 
with  a  suspension  of  the  6th,  prepared  by  the  3d  and  resolved  to 
the  5th.  At  (b)  the  chord  of  preparation  is  in  the  second  inversion, 
and  the  chord  of  suspension  and  resolution  in  the  third  inversion.  At 
(d)  the  suspension  occurs  in  the  alto,  and  at  (e)  in  the  bass. 

The  following  exercises  should  be  worked  out  by  Rules  III  and  IV, 
observing  closely  the  restrictions  given  above. 

232 


3 — 6- 


5 — 9 — 8 
-3  3- 


le 


-1^ 


ZJ 


-*■  s 


etc. 


"m- 


^^=i^ 


-(2- 


V^'rr 


6  4 
3 
N 


I 

N3 


l\8 


N3 


#6 
4 
3 
K 


SUSPENSIONS 


III 


i 


:^=z:i5 


^=?=F 


'i-^^zi— ^ 


-<56. 


f^ 


^ 


*: 


-(2- 


frri'    I   <y      -fa-4- 


-^ fii- 


233 

n 

I     ,    + 

"f* — r5 — ^r- 

H r 

^ 

-J       J 

H-^-?^^ 

|)^  r  r  r 

-h  r  i 

^-^  J  J 

-^- 

^^^-K 

""^  r 

I 


:^ 


-^—9^ 


-(5^ 


^ 


111.  No.  37 


L.  M.  GoTTSCHALK,  "Last  Hope" 

3 6— 5 


^33 


ffi 


^^ 


i 


ga . 


"^i^ S^ 


-ss:: 


ilAzS: 


^1 


^^ 


=«^ 


? 


¥ 


When  a  suspended  note  is  affected  by  an  accidental,  a  similar  sign 
should  be  placed  before  the  symbol  of  suspension  in  the  bass  figuring, 
thus: 


234 


-4 3 


-6 5 


i 


-i?^^^J— J- 


^ 


"^ 


-a- 


^•=12^ 


J— J- 


(O 


-g^- 


K3 


4 


«  6 

#N3 


g 


|i6 
4 
3 


At  (a)  the  note  of  resolution  (the  D  3d,)  is  preceded  by  a  suspension 
of  the  depressed  note  above,  Eb.  At  {b)  the  note  of  resolution  (C#, 
figured  ^6)  is  preceded  by  a  suspension  of  the  note  above,  which  is 
not  chromatically  altered.     At  (c)  the  note  of  suspension  is  indicated 


112 


CUMULATIVE   HARMONY 


as  a  4th  affected  by  a  sharp  (C#).  At  (d)  the  suspension  occurs  in  the 
bass,  where,  with  a  chord  of  4,  the  actual  bass  F^,  as  the  resolution 
of  a  suspension,  is  preceded  by  a  suspension  a  degree  higher,  which  is 
affected  by  an  accidental  sharp  (G^).  The  relative  position  of  mem- 
bers of  a  chord  may  be  changed  to  provide  a  preparation  for  a 
suspension. 

235 

7 4 3  7 4 3 


i 


w 


f- 


m\ 


.i=^ 


Te 


-(2- 


a 


ip: 


Jll 


b7 


br\3 


b6 

bK 


Two  examples  are  here  given  of  the  primary  note  ascending  a  fourth, 
inviting  a  passing  modulation  in  which  the  addition  of  the  7  th  pro- 
vides a  preparation  for  a  suspension  of  the  4th  in  the  second  chord. 

Occasionally  the  bass  note  changes  to  another  note  of  the  chord 
simultaneously  with  the  entrance  of  the  resolution  of  the  suspension. 


236 


i 


-«*- 


J 


^: 


^ 


J2^ 


^ 


K8 
6 
4 


N6 
b5 


lU.  No.  38 


Gluck,  "  Orpheus  " 


SUSPENSIONS 


"3 


Double  suspensions  are  formed  by  combining  Rules  I  and  III,  or 
II  and  IV.     Other  suspensions  of  this  species  will  be  given  later. 


237 


m.  No.  39  W.  H.  NiEULiNGER,  "  The    Bumblebee  " 

5 9 8 

7 4 3 


i 


e= 


f=r 


ip  C    £- 


3: 


\-^      X" 


£ 


f 


:^^: 


^ 


JSt- 


The  following  exercises  are  appended,  to  be  worked  out  with  sus- 
pensions according  to  the  four  rules  given  above. 

238  + 


r4=T: 


r;^ (^—\ 

r^ 

+ 

r*^ 7n — 1 

r^^— 

-^ j 

^ — f 

r^     (^ 

T^ f^ 

1 f^ 

-<© 

|..       ' 

' 

j         1 

1 

i      ! 

1 

' 

1^ 


-(^ 


-fa- 


-^ — fs 


?2=;^ 


-t=f: 


I 


239 


e 


:te 


:2z: 


-(s — (Z- 


1 


^:fe^z=^ 


^-^ 


? — ("^Ir^  r  I  r  P  \^- 


i^ 


I 


240 


114 

241 


CUMULATIVE   HARMONY 


m 


lr:^=f^f=r^ 


ii: 


0^f  0  L 


If 


& 


Add  the  three  upper  voices  to  the  following  bass  sets,  employing 
suspensions  of  the  various  species  (with  classification  figuring). 
Transpose  to  numerous  keys  for  similar  treatment. 


242 


^^^i^=;ribi   J  \^^  ll^ 


w^ 


-^-. 


:^ 


||4         7 


^6 
4 


^e^       rj- 


-25^ 

1|6 

lis 


243 

Key 


6 
5b 


of  e 


b6 
b5 


-?5l- 


-^^ 


Ik 


#6 
4 
3 


Pg* 


6 


II  '  111         ^ 


'|6 

lis 


mi 


t 


244 


111 


S6 
4 


[11 


3 


ifi 


E^feE^^^E 


teei^^-^iO, 


^ 


|]7        6       [6_ 
b5 


I 


lidJat^it 


!l' 
iJl 


(S^-r- 


1    6    t  111    !    7 


CHAPTER   XX 
RETARDATIONS,   OR  ASCENDING    SUSPENSIONS 

Retardations  are  similar  to  suspensions,  except  that  they  resolve  by 
ascending  one  staff  degree  to  the  note  of  resolution,  instead  of  de- 
scending, as  in  the  case  of  the  latter. 

The  resolution  may  be  heard  in  the  bass  during  the  life  of  the  sus- 
pension, at  a  distance  of  a  7th  or  more. 

Retardations  are,  in  general,  much  less  agreeable  to  the  ear  than 
are  normal  suspensions,  and  of  less  frequent  occurrence.  Disso- 
nances, as  a  rule,  are  acceptable  only  when  they  progress  downward 
one  staff  degree  to  a  consonance.  Normal  dissonances  of  suspension 
are  agreeable  for  this  reason,  and  because  during  their  existence  the 
hearer  experiences  the  anticipation  of  a  well-defined  resolution. 

Among  retardations,  those  that  progress  by  a  minor  second  to  the 
note  of  resolution  are  the  most  acceptable,  those  progressing  by  a 
major  second  rarely  serving  to  enhance  the  beauty  of  the  harmony. 

Of  the  progressions  by  a  minor  second,  the  seventh  of  the  scale 
resolving  to  the  octave  is  the  most  popular,  although  the  third  of  the 
scale  to  the  fourth  in  the  major  keys  and  the  second  to  the  third  and 
the  fifth  to  the  sixth  in  the  minor  are  often  used,  particularly  in 
combination  with  normal  suspensions. 

The  uninviting  progression  of  a  major  second  in  the  resolution  of  a 
retardation  has  led  composers  to  modify  the  harshness  and  relieve 
the  uncertainty  of  the  anticipation  by  chromatically  elevating  the 
note  of  suspension.  By  this  means  the  anticipation  of  the  resolution 
becomes  more  intensified  and  quite  definite  through  the  preferred 
progression  of  a  minor  second.     Examples  of  this  form  will  follow. 

The  symbol  for  retardations  is  the  radical  (i/)  inclined  upward, 
indicating  that  the  note  on  the  diatonic  degree  below  has  been 
retarded. 

Rule  I.  When  a  primary  note  ascends  a  fourth,  we  may  retard 
the  7th,  prepared  by  the  3d  and  resolved  to  the  8va. 

"5 


ii6 


CUMULATIVE    HARMONY 


245 


At  (a)  the  3d,  as  a  preparation,  is  sustained  at  (b)  as  a  retardation 
of  the  7th,  resolving  at  (c)  to  the  8va;  the  classification  figures 
above  indicate  a  retardation  of  the  7th,  prepared  by  the  3d  and 
resolved  to  the  8va,  with  the  symbolized  figuring  below  showing  a 
retardation  below  the  8va.  At  (d)  is  an  example  of  the  retardation 
of  the  7th  in  the  bass,  figured  as  a  retardation  below  the  actual  bass. 


lU.  No.  40 


Haendel,  "  Messiah  " 
3 7—8 


in.  No.  41 


James  H.  Rogers,  "Rubaiyat  of  Omar  Khayyam" 
3 7 8 

r^,     8va 


.fe|t=f£^=fc:5^ 


Rule  II.  When  a  primary  note  is  followed  by  another  a  fifth 
higher,  we  may  retard  the  6th,  prepared  by  the  3d  and  resolved  to 
the  7  th. 


RETARDATIONS,   OR   ASCENDING   SUSPENSIONS      117 

246 


« 


3- 

I. 


{a) 


-zi- 


f=f= 


I 


VI 


4 
VZ 


At  {a)  is  an  example  of  the  retardation  of  the  6th,  prepared  by  the 
3d  and  resolved  to  the  7th;  at  (6),  the  same,  with  the  chord  in  its 
second  inversion  and  the  retardation  in  the  alto. 


m.  No.  42 


Larshetto 


r^ 


Beethoven,  "  Symphony  II  " 
3 6 7 


^ 


-^ ^-— ^ 


^ 


3=^ 


S 


Rule  III.  When  a  primary  note  is  followed  by  another  a  fourth 
higher,  we  may  retard  the  2d,  prepared  by  the  5th  and  resolved  to 
the  3d. 

247 


i 


(a) 


(^) 


1^3 


6 

1/ 


At  (a)  is  a  retardation  of  the  2d,  prepared  by  the  5th  and  resolved 
to  the  3d,  indicated  5 — 2 — 3  and  figured  as  a  retardation  below  the 
3d;  at  (6).  the  same  retardation  in  the  bass,  figured  as  a  retardation 
below  the  actual  bass  in  a  chord  of  \ . 


ii8 


CUMULATIVE   HARMONY 


111.  No.  43 


Larghetto 


Beethoven,  "Symphony  IT 
5 2 3 

3 7 8 


m- 


ifEE^EEf 


i 


w- 


x^ 


^^ 


Rule  IV.  When  a  primary  note  is  followed  by  another  a  fifth 
higher,  we  may  retard  the  4th,  prepared  by  the  8va  and  resolved  to 
the  5  th. 

An  application  of  this  rule  is  here  given,  with  the  retardation  in  the 
soprano. 


248 


-Ki- 


m. 


si- 


6 
1/3 


in.  No.  44 


Gluck,  "  Clemenza  " 


^^=i^ 


'->  r 


1 1 
f^' 


%ii 


^-^ 


3i= 


-tp^ 


0  0^ 


^ 


Retardations,  by  the  above  four  rules,  are  equally  suitable  in  all 
respects  for  use  in  minor  keys. 

Work  out  the  following  exercise  after  the  four  rules  in  various  keys. 


RETARDATIONS,    OR    ASCENDING    SUSPENSIONS       119 


249 


i 


UU- 


>     g^ 


«^zi^ 


r 
■J- 


m 


■^z 


^ 


^ 


^ 


etc. 


^—(>- 


-a- 


6 

L/3 


1/3 


6 
1/3 


U^3 


#6 
4 
3 


1/8 


ill 


i 


:fe 


^gEEfe 


:^ 


P 


:^ 


'^~rl^' 


i 


1=^ 


Double  and  triple  suspensions,  or  retardations,  or  combinations  of 
suspensions  and  retardations,  are  fully  suitable  for  use  as  the  occasion 
may  seem  to  demand,  providing  they  are  used  with  due  regard  for 
prescribed  limitations. 


250 


-4- 


-2 3 

-7 8 


i 


■75^ 


(«) 


{b) 


{c) 


-i 


-d- 


K8 

N3 


I\5 
N3 


ii 


^ 


:J:=^ 


1/8 

1/3 

—9 8 

—4 3 

-7 8 


^ 


f 


-j- 


C'^) 


>^'"J 


J 


i^z: 


1/8 

K3 


N6 

4 

VZ 


T 


K8 
K3 
1^8 


I20 


CUMULATIVE    HARMONY 


At  (a)  we  have  an  example  of  a  double  suspension  of  the  4th  and 
9th;  at  (b),  a  double  suspension  of  the  4th  and  6th;  at  (c),  a  double 
retardation  of  the  2d  and  7th;  at  (d),  a  combined  suspension  and 
retardation  of  the  4th  and  7  th;  at  (e),  a  combined  suspension  and 
retardation  of  the  4th  and  6th;  at  (/)/  a  combined  double  suspen- 
sion and  retardation  of  the  4th,  7th,  and  9th. 

m.  No.  45      Mendelssohn,  "  Quartette  in  A  Minor,"  op.  13 

3 7 8 

a 9 — 


Chord  suspensions  are  also  to  be  found  occasionally  when  all  voices 
are  included. 


251 

tf — ^ 

^=5 — 

->i J 

1/8 
K3 


Retardations  by  Rules  III  and  IV,  in  the  major  mode,  and  II  and 
IV,  in  the  minor,  which  resolve  by  whole  steps,  may  be  chromatically 
elevated  above  their  respective  preparations,  in  order  to  intensify 
their  progressions  to  the  notes  of  resolution. 


252 
5- 


t) 


(a) 

-r— 
#1/3 


-^^ 


=#^ 


(^) 


ifV3 


-Kh 


f- 


W1 


^^ 


{d) 

I 


6 
5 

#1/3 


RETARDATIONS,  OR  ASCENDING   SUSPENSIONS       121 


i 


3t: 


-4^ 


r- 


,U: 


Pt 


fe 


ie) 


M^^ 


A 


if) 


^ 


m 


fl/3 
1/8 


6 

1/5 
:i/3 


6 

Sl/5 


At  (a)  is  an  elevated  retardation  of  the  2d;  at  (6),  of  the  4th;  at 
(c),  of  the  6th,  in  a;  at  {d),  of  the  4th,  in  a;  at  (e),  a  double  retardation 
of  the  2(1,  elevated,  and  the  7th;  at  (/),  of  the  4th,  elevated,  and  the 
6th;  and  at  (g),  a  double  retardation  of  the  6th,  elevated,  and  4th, 
elevated,  in  e. 


in.  No.  46 

Andante  con  ntoto  3 6  —  7 

S  8 4 5 


|E£ 


■&. 


Mozart,  "Quartette  in  Eb" 
5  2 3 

^ 3-— 7 — 8     > 


I-J 


e 


■■  ?=y 


O: 


:^ 


ir 


111.  No.  47 


Bekthoven,  "  Symphony  II  " 


Work  out  the  following  exercise,  employing  the  elevated  retarda- 
tions in  various  keys. 


122 


CUMULATIVE   HARMONY 


253 


'M^^ 


+ 


-(2- 


— 4 — 3 


3- 
-2 3 


— 6 5 


5- 
-4 — 5 


-2 3 


-7 8 


BE^E* 


-^— J- 


I        I 


t^ 


f^ 


(i 


J 


etc. 


3 


T-|g- 


-iSZ- 


#V3 


K8  SL/5 

6 
4 


#1/3       S6      ftva         6 

4  5 

3  K 


(2 ^5 


^ 1^ 


-(2 «-- 


-(2 (Z- 


iit 


-^5! &Si 1 fS? (22 ^ — ^- 


-(S^ 


Work  out  the  exercises  given  in  the  chapter  on  suspensions,  as 
accompanied  melodies,  using  retardations  in  like  manner. 


CHAPTER   XXI 

PASSING  NOTES 

A  passing  note  is  a  diatonic  embellishment  used  in  passing  melodi- 
cally  from  one  harmony  note  to  another  a  third  above  or  below  it. 

254 


B3 


nn  ni  r. 


J: 


-s*- 


^ 


f 


(*) 


J-  -i 


(O 


S 


P=fcfcfc^ 


f= 


=&=9^ 


11 


At  (a)  the  passing  note  D  occurs  between  the  two  harmony  notes 

C  and  E.     At  (b)  the  passing  note  B  occurs  between  two  harmony 

notes  of  different  chords.     At  (c)  the  passing  note  occurs  in  the  bass, 

and  at  (d)  in  the  tenor. 

ni.  No.  48  Beethoven,  "  Sonata,"  op.  22 

Adagio  con  molto  espressione 

-  b#_  ^  ^  ^       ^ 


W 


^ 


g 


& 


m^^^R^^^-tt^i 


^-^-* 


m.  No.  49 


X.  ScHARWENKA,  "  Minuet,"  op.  18 


P^ 


^ 


i 


■J 


r:^ 


k 


^  i 


"3 


124 


CUMULATIVE   HARMONY 


Passing  notes  niay  be  accented   (a),  or  unaccented   (b). 

255 


(a) 


(a) 


(i) 


ib) 


-^ ^ 


S  » 


tJ 


imi 


-7^- 


-^- 


Successive  passing   notes   may    occur,  with  the  T  chord,  between 
the  fifth  of  the  scale  and  the  octave,  ascending  or  descending. 


256 


'=^=^z 


.m:^ 


m.  No.  50 


Schumann,  "Album,"  op. 


*An  example  of  successive  passing  notes. 


What  is  said  of  passing  notes  occurring  in  the  accented  or  un- 
accented parts  of  the  bar  or  beat  is  true  of  all  succeeding  species  of 
embellishments. 

In  the  minor  mode,  in  order  to  escape  the  disagreeable  ascending 
augmented  second,  the  sixth  of  the  scale,  as  well  as  the  seventh,  is 
generally  elevated,  thus  effecting  what  is  frequently  termed  the 
melodic  form  of  the  ascending  minor  scale. 


PASSING   NOTES 


125 


257 

1        i    li  I     ^ 

(O 

J               1 

^5* 

1 

* ^ 

25> 

^-f^ ^- 

^ f^ 

'-f f— " 

At  (a)  is  an  example  of  successive  passing  notes  between  the  fifth 
of  the  normal  scale  and  the  octave  in  the  key  of  a.  The  normal  sub- 
tonic,  G,  through  its  isolation  of  a  whole  step  from  the  Tonic,  lacks 
in  ascending  tendency;  it  consequently  fails  in  the  capacity  of  a 
leading  tone,  which  is  an  important  melodic  function  of  this  degree  of 
the  scale.  The  elevation  of  the  subtonic  gives  it  a  leading-tone 
quality,  strongly  inviting  an  ascending  progression  to  the  Tonic  {b). 
Here  again,  however,  the  melodic  tendency  upward  of  this  passage  is 
interrupted  by  the  normal  sixth  of  the  scale,  F,  which,  because  of  its 
proximity  to  the  fifth,  E,  has  a  tendency  downward;  this  fact,  com- 
bined with  the  unmelodious  ascending  progression  of  an  augmented 
second,  makes  the  elevation  of  the  sixth  of  the  scale  {c),  as  well  as 
the  seventh,  in  a  passage  from  the  fifth  of  the  minor  scale  to  the 
octave,  practically  a  melodic  necessity. 

This  is  true  more  particularly  in  vocal  music;  in  instrumental 
music,  the  elevation  of  the  seventh  only  is  frequently  practiced. 

The  successive  passing  notes  descending  between  the  octave  and 
the  fifth  of  the  scale  may  be  employed  without  elevation  of  the  sixth 
and  seventh,  or  with  elevation  of  the  seventh  only,  the  progression  of 
the  augmented  second  descending  being  melodically  quite  satisfactory, 
as  well  as  serving  to  aid  in  identifying  the  minor  mode. 


258 


i 


T 


f- 


:?£: 


T 


126 


CUMULATIVE   HARMONY 


111.  No.  51 


Haendel,  Overture,  "Messiah" 


1^^=^ 

-j^S>f^    J 

=^ 

V^^ 1—      K 

— ^' 

1 

— «— 

1- 

-^ J 

— <9 

-^ " 

\F— ^ 

1 — ^^ . — 

m 

-^ 1 

^  6 

2 


^ 


An  extended  consideration  of  the  various   forms  of  minor  scales 
would  seem  to  be  quite  in  place  at  this  time. 


^ — a- 


{b) 


&.       'g 


^ 


i 


(O 


g.        ^- 


n ^ 


e>      ^g 


1^-4^ 


I.  The  first  reference  was  to  the  normal  minor  scale,  consisting  of 
whole  steps  except  between  two-three  and  five-six,  that  is,  as  indi- 
cated by  its  signature  (a). 

II.  With  the  introduction  of  the  D  chord,  the  seventh  of  the  scale 
is  necessarily  elevated  from  the  signature  indication,  in  order  that 
the  third  from  the  fundamental  of  that  chord  may  be  major  (6), 
thus  causing  the  subtonic  to  serve  as  a  leading  tone. 

This  forms  what  is  commonly  known  as  the  harmonic  minor  scale, 
although  it  may  be  considered  merely  as  a  table  of  the  notes  em- 
ployed harmonically  in  that  key. 

III.  With  the  introduction  of  passing  notes  the  melodic  element 
enters  freely,  and  by  their  aid  we  are  enabled  to  construct  the  ascend- 
ing melodic  scale  with  the  sLxth  and  seventh  elevated  and  the  half 
steps  between  two-three  and  seven-eight  (c).  While  this  form  is 
generally  employed  with  the  T  and  D  chords,  it  is  impracticable 
with  the  S  chord,  as  the  normal  sixth  of  the  scale  is  an  essential  mem- 
ber of  that  chord  and  is  not  subject  to  alteration.  The  form  best 
suited  for  employment  with  the  S  chord,  both  ascending  and  de- 
scending, is  the  normal  scale,  although  the  seventh  is  frequently 
elevated  in  both  directions. 


111.  No.  52 

Andante 


PASSING   NOTES  127 

Mozart,  "  Rondo  in  A  Minor  " 


111.  No.  53      W.  W.  Gilchrist,  "  Home  they  Brought  her  Warrior  Dead" 


^^ 


^ 


-^ — W 


-4^=^ 


All    her 


maid-ens  watch-ing 


said  She   must 


weep    or     she    will 


die 


^^ 


^^ 


-U 


W^^^^ 


W- 


-0 — m- 


^ 


-<9— 


M^. 


-si- 


% 


ni.  No.  54 


Gilchrist,  "Dolphin  Lullaby" 


S 


m 


H* &* 


p=t4 


g 


3 


;^b   f      b. 


J— t;J |J 


:?E=l; 


111.  No.  56 


Beethoven,  "  Sonata  Appassionata,"  op.  57 


^a^NT^^i^ 


^e3S 


4- 


^^ 


r 


^ 


lis 


1 


A  classification  of  the  minor  scales  to  be  used  melodically  with  the 
three  primary  chords  is  as  follows: 


128 


CUMULATIVE    HARMONY 


With  the  Tonic  chord :  ascending,  the  elevated  sixth  and  seventh, 
and,  occasionally,  the  elevation  of  the  seventh  only  ;  descending,  the 
seventh  elevated  and  the  normal  scale  (a).  (Also,  conforming  with 
certain  ancient  modes,  ascending  as  a  normal  scale.) 


260 


(a) 


^— ^ 


m      P 


M^=f^ 


iEE 


0       P- 


t^^^^T-f-t    r    .    -A 

t-"^r-r-f^-T=^=T 

Ifl^                            'ill* 

W — ^ — 1 — \ — \— 

^-g 

-^ 

With  the  Suhdominant  chord :    ascending  and  descending,  the  nor- 
mal scale,  and  at  times  the  elevated  seventh  (b). 


• — p 


V- 


/rff '  i  r 

_A_^           _^ 

pr^'-^>^-,   --n 

'^^-r^ 

^    ■  ^  '^^^4 

^ 

s^   ^ 

PF«7^  //?e  Dominant  chord :  ascending,  the  elevated  sixth  and 
seventh,  and,  occasionally,  the  elevated  seventh  only;  descending, 
the  seventh  only  (c). 


PASSING   NOTES 


129 


(O 


m 


:M^^ 


-t«-r^ 


S=P= 


m 


# 


g 


(N^ 

it^r  r  #  ,  I n 

'   '   1   r  ^f=Mi 

m                   f 

Faulty  consecutives  or  other  improper  progressions  may  not  be 
formed  by  passing  notes,  nor,  in  fact,  by  embellishments  of  any  kind. 


Passing  notes  may  not  proceed  by  degree  to  a  unison  (a)  unless  -^ 
they  appear  as  compound  passing  notes  (6). 

Passing  notes  proceeding  by  degree  to  an  octave  (c)  are  not  ob- 
jectionable. 

Compound  passing  notes  consist  of  passing  notes  occurring  in  two 
voices  simultaneously,  as  at  (d). 

in.  No.  56  Cesti 


i 


[E^ 


-0- 


=i»=iF 


-/ 


-f^    0     ^  -f- 


m 


i 


3^ 


r 


I30 


CUMULATIVE   HARMONY 


ni.  No.  57 


Frederick  Field  Bullard, 
"  The  Lass  of  Norwich  Town  " 


M 


m 


|5 


f- 


^ 


r 


t  ^i  '\ 


111.  No.  58 


Chopin,  "  Nocturne,"  op.  27,  No.  2 


8va- 


Compound  embellishments  should,  in  general,  be  consonant  one 
with  another. 
Passing  notes  may  be  repeated,  as  at  {a). 


262 


{a) 


{a)  {a) 


i 


T^J^T^ 


r 

4 


j 


-i 


Work  out  the  following  exercises,  employing  passing  notes  singly 
in  alternate  voices.  Cause  the  basses  to  move  by  skip  of  a  third, 
where  practicable,  to  aid  in  presenting  opportunities  for  embellish- 
ments.    Compound  passing  notes  also  may  be  occasionally  used. 


PASSING   NOTES 


131 


268 


;l^,  .n  J  J    =^ 

^J — J — i^ — ^ 

\^  r  ~t~r 

'WJp-*^ ^ — J— 

LJ  r    r — ^ 

iN^<'    ft » — » — ' 

'^    1             Lj    I 

C                                   0 

— T" ^ — F— i 

i 


^t=^ 


*=fi 


:*==!> 


^ 


1= 


ii 


i 


etc. 


g — *-^it — ^ 


r  I I 


II 


\n 


b7 


i 


sfrn±] 


=ttF: 


-<2- 


•<^  +         +. 


^i^ 


3 


+      + 


~F      0- 


=^==^ 


^ 


I 


^ 


^^  g 


264 


^^m 


If*  If  r  r  p 


-^» — ^ 


£^ 


g 


^'» — «- 


^ 


ip: 


^ 


=i?==F 


¥ 


i 


+ 


# a P — r«^ 


CHAPTER  XXII 


CHROMATIC  PASSING  NOTES 

A  chromatic  passing  note  is  a  chromatic  embellishment  used  in 
passing  melodically  from  one  harmony  note  to  another  a  major 
second  above  or  below  it. 

265 


:^^^^^^|S 


4 


fe 


^ 


{a) 


A^F- 


ib) 


:J: 


(O 


-z?- 


^s 


-f:^- 


At  (a)  appears  a  chromatic  passing  note  between  the  harmony 
notes  C  and  D,  followed  by  others  in  the  soprano.  At  {b)  is  a  chro- 
matic passing  note  in  the  alto,  and  at  (c),  a  chromatic  passing  note  in 
the  bass. 

The  following  given  melody,  called  a  germ  set,  is  to  be  harmonized 
in  such  manner  as  to  present  the  best  opportunities  for  the  employ- 
ment of  passing  notes  and  chromatic  passing  notes  tending  toward  the 
formation  of  a  continuous  eighth-note  motus  in  alternate  voices.  By 
motus  is  meant  the  melodic  change  of  one  or  more  voice  parts  from 
one  pitch  to  another ;  when  such  changes  take  place  in  a  continuous 
succession  of  eighth  notes,  a  continuous  eighth-note  motus  is  presented. 

Transpose  to  other  keys  for  similar  exercise. 


266 


^i 


-d=^ 


^ 


1 


te 


132 


CHROMATIC   PASSING   NOTES 


133 


J   J   ^  \>¥  W 


:J=^ 


^ti 


f=»r 


r 


1=1 


J33- 


#2= 


DU^ 


etc 


S 


^ 


^g 


^ 


^»==s 


W 


i 


M 


m 


111.  No.  50 


Mozart,  "Rondo  in  A  Minor" 


35 


m 


m 


IS: 


11 


m 


VKt^i^lV      J^:iy:Ua^ 


An  extended  passing  note  is  an  embellishment  used  in  passing  melodi- 
cally  from  one  harmony  note  to  another  more  than  a  third  distant,  in 
such  manner  as  to  approach  the  second  note  by  degree  from  the  side 
upon  which  the  first  is  located.  The  approach  should  be  diatonic 
from  above,  and  chromatic  from  below. 

267 

(a)  (d)  ic)  (d) 


i-^^^^^-t^ 


/«S=J: 


J. 


:^ 


-i9- 


A 
^ 


134 


CUMULATIVE   HARMONY 


At  (a)  an  embellishment,  A,  is  used  in  passing  melodically  from  the 
harmony  note  C  to  another  harmony  note,  G.  It  approaches  the 
second  note,  G,  by  diatonic  degree  from  the  upper  side,  the  side  upon 
which  the  first  one  is  located.  At  (b)  the  extended  passing  note  D# 
approaches  the  harmony  note  E  chromatically  from  below,  the  side 
upon  which  the  preceding  harmony  note  is  located.  At  (c)  the  ex- 
tended passing  note  F  approaches  the  E  diatonically  from  above, 
and  at  (d)  a  similar  embellishment,  B,  approaches  the  harmony  note 
C  chromatically  from  below. 

m.  No.  60  Hector  Berlioz,  "  Faust " 


An  extended  passing  note  may  be  used  between  two  harmony 
notes  a  third  apart,  providing  it  ascends  to  the  second  note  chromati- 
cally altered  from  below,  as  at  (a)  (a). 

268 

(a)  (a) 


m.  No.  61 


M 


Schumann,  "  Novellette,"  op.  21,  No.  2 
3 


^ 


^ 


r=#= 


w 


-^-^ 


^ 


■rr«! 


wH^ 


^*^ 

^ 


nS3- 


m^m 


ai. 


i^- 


CHROMATIC    PASSING   NOTES 


135 


The  following  exercises  may  be  worked  out  in  several  keys,  using 
extended  passing  notes,  after  which  passing  notes  and  chromatic  pass- 
ing notes  may  be  added  to  form  a  continuous  eighth-note  motus  in 
alternate  voices. 


2eo 


J^-fS-.^ 


^^eM,^^ 


<■ «'  J  J  ^  ^^ 


-J — 


¥ 


le 


-s^- 


^^ 


i 


etc. 


-M 


r=^ 


^m 


11         III'       6 


^ 


i 
i 


fe 


#i^ 


^  >g 


F      <y- 


-^ ^ , ^ ^ 

« 


g 


I 


270 


^ 


:^     I       f 


? 


^ 


i 


#: 


E^ 


^ 


Jit 


:i^ 


«f{r  J  jrir-t^'^irJ  j  rit^-^^s 


^^ — ±- 


NW  '   r  r  If  p  r  r  iJ  I   r 


I 


CHAPTER  XXIII 


AUXILIARIES 

An  auxiliary  is  an  embellishment  located  a  degree  above  or 
below  a  harmony  note,  which  precedes  and  follows  it.  It  is  diatonic 
above  and  chromatic  below  the  harmony  note.  (Chromatic  aux- 
iliaries above  are  occasionally  used  by  composers.) 


271 


(a) 


ib) 


(O 


{d) 


i 


is 


:#* 


-7:i- 


f- 


r 


-J- 


-1^ 


H=2- 


r 


r 


At  (a)  and  (c)  are  auxiliaries  above,  and  at  (&)  and  (c?),  auxiliaries 
below.  In  each  case  the  embellishment  is  preceded  and  followed  by 
the  harmony  note  upon  which  it  depends  for  existence. 

Work  out  the  following  exercises,  using  auxiliaries  above  and  below 
wherever  practicable.  Subsequently  add  preceding  embellishments 
to  form  a  continuous  eighth-note  motus,  first,  in  the  soprano,  then 
in  the  alto,  tenor,  and  bass  in  succession;  this  may  be  done  also  in 
alternating  voices. 

272  ' 

Germ  Set 


s^ 


(ie^^ 


1e 


1 


-0-        ~0-  -M- 


X3-J^ 


^i2- 


a 


^-(2- 


^ 


6 

b5 


ill 


136 


AUXILIARIES 


137 


w=m 


^ 


^ 


(i 


^=^i53=J 


^:3. 


g 


* 


:*S 


J: 


J 


J^ 


etc. 


£ 


-ft]*^ 


•^       7 


I 


273 


^ 


^^;^ 


'^^ 


^ — (^ 


ip: 


\-T^—t 


l^ 


=F 


Note.  When  embellishments  are  to  be  employed  in  the  soprano,  three  staves 
should  be  used,  in  order  that  the  given  germ  set  may,  for  comparison  and  analysis, 
remain  unchanged. 

m.  No.  62  Mozart,  "  Variations  " 

5 


(^ 


r  i^r^-r  )^^ 


:?:-»-  -r-  ^  -r  )^  -r 


— ^H'  r  ^  ^  ^^  f -^ 


138 


CUMULATIVE   HARMONY 


The  auxiliaries  below  the  third  and  the  seventh  of  the  scale  in  the 
major  mode,  and  below  the  second  and  the  fifth  of  the  scale  in  the 
minor,  may  be  diatonic. 

Auxiliaries  a  diatonic  whole  step  below  these  notes  are  particu- 
larly satisfactory  when  used  in  melodic  connection  with  auxiUaries 
a  diatonic  half  step  above. 

The  auxihary  below  the  seventh  degree  of  the  minor  scale  may  be 
a  chromatic  whole  step. 

Occasional  examples  are  to  be  found  of  auxiliaries  a  diatonic  whole 
step  below  the  second  of  the  scale  in  both  major  and  minor  modes. 

274 


i 


-s 


w 


-A 


{a) 


J 


A 


ib) 


-5*- 


-42- 


^ 


i 


^ 


1^ 


-^m^ 


-G>- 


{c) 


{d) 


r 


(^) 


m 


-Tir 


^ 


^ 


'¥- 


-(^ 


#6 
4 
3 


At  {a)  is  given  an  example  of  the  auxihary  below  the  third,  and  at 
(&)  of  the  auxihary  below  the  seventh,  of  the  major  scale.  At  (c) 
and  {d)  are  examples  of  the  auxiliary  below  the  second  of  the  scale 
in  major  and  minor  modes.  At  {e)  is  shown  the  auxihary  below  the 
seventh  of  the  minor  scale  as  a  chromatic  whole  step. 

m.  No.  63  GiuLio  Caccini,  1546-1614,  "  Madrigal  " 


AUXILIARIES 


139 


An  illustration  of  the  auxiliary  below  the  seventh  degree  of  the 
minor  scale  is  here  presented. 

Work  out  Exercise  272  with  the  eighth-note  motus  in  the  bass  and 
in  the  tenor,  as  in  the  following  models: 


276 


.t=^ 


J- 


Eg 


T 


J 


J 


-"^r-f^m—m-^s^ 


J 


i^E 


?=^*=f^ 


;s 


i 


t 


HI 

J 


i 


f- 


J. 


-i. 


-i 


11 


^  #  ^ 


?=^ 


tF=F 


It 


He 

4 


4         6 

2 


6  6 

4 


^ 


g 


I 


276 

r^ ^ 

1 

— ^ 

y^r         r    ^ 

r     ^-r- 

— • 

J  I  J  V  -"^  J-  J 

^    J  -  :^-  X: 

«-J-   - 

\  ^4P--  ^ j5 

|6                 i                   1 

I40 


CUMULATIVE   HARMONY 


/^^ 


r 


W-^- 


J  ^  J 


4 


Successive  auxiliaries  may  occur  above  the  fifth  or  below  the  first 
of  the  scale  with  the  T  chord,  involving  the  use  of  the  sixth  and 
seventh  of  the  scale  as  embellishments. 


277 


ii-+-^n-+^ 

M      ^-Hi 

f^\   m        •      ^     ^ 

^  •           ^     m     ^\ 

m           '^         ^         H        A 

I  l^"  7    ^                '                    ^ 

«                ,                        ^          <5. 

< 

-s>- 

-G>- 

/m)' 

VfJ- 

vr^  '^ 

rJ 

Si 

\ 

In  the  minor  mode  successive  auxiliaries  above  the  fifth  should 
be  from  the  normal  scale  (a)  (a)  and  below  the  first  with  elevated 
sixth  and  seventh  {h)  (b).  Normal  scale  successive  auxiHaries  above 
the  fifth  occasionally  occur  with  the  Dominant  D  chord  (c)  (c). 


'^=^     »     ^: 


-7S)- 


(a) 


-75^- 


^f=M: 


-f^- 


:i 


1^ 


r 


i^) 


AUXILIARIES 

|(0 


141 


m 


(g    II     >s^ 


(c) 


^ 


-&- 


* 


tt 


r  U  r 


r 


r 


:i 


^ 


-s?- 


J 


<5i!- 


f" 


m.  No.  64  Henry  Hadley,  "  The  Nightingale  and  the  Rose  " 

A  lle^retio  grasioso 


m 


f^^       ij       I   =t 


»g^± 


^     :^ 


^  ; 


^ 


111,  No.  65 


David  Stanley  Smith,  "  The  Dark  " 

3 6—5 

8 4 3 


i 


i 


i^ 


p 


=^ 


•^^-t 


? 


cj  r  g 


"TT 


tET 


r 


J>- 


fl^s 


t^^ 


s 


^ 


g 


^ 


p= 


r 


r- 


r 


r- 


An  extended  auxiliary  note  is  used  in  passing  melodically  from 
one  harmony  note  to  another,  approaching  the  second  note  by  de- 
gree from  the  side  opposite  that  on  which  the  first  is  located.  The 
approach  should  be  diatonic  from  above,  and  chromatic  from  below. 


279 


^ 


{a)  {b)  (O  {d) 

(^     r,     r  ^^^ 
'    [    -J-     I 


(«) 


r 
f- 


A 


m 


142 


CUMULATIVE   HARMONY 


At  (a)  is  an  extended  auxiliary  above  the  harmony  note  E,  which  it 
approaches  from  the  side  opposite  the  first  harmony  note,  C.  At 
(b)  is  an  extended  auxiliary,  B,  below  the  second  harmony  note,  C;  it 
is  preceded  on  the  opposite  side,  above,  by  the  harmony  note  E. 
At  (c)  is  an  extended  auxiliary,  F#,  below  G;  and  at  (d)  an  extended 
auxiliary,  C,  above  B.  At  (e)  is  an  extended  auxiliary  below  the 
seventh  (as  a  leading  tone)  of  the  minor  scale. 


m.  No.  66 
Allegro 


Beethoven,  "  Sonata,"  op.  14,  No.  2 


^^ 


S 


3 


■¥■ 


te 


M 


1     [:.£, 


'^^ 


in.  No,  67 


8 


Chopin,  '\Polonaise  in  Eb,"  op.  22 


^-Jtl 


-^ 


•= Nil- 


^ 


w^ — ^ 


~ri   ^n 


!s 


*    ^ 


^ 


#i^-^-^^ 


^^ 


kd* 


=2^ 


^=^ 


^ 


^^ 


=a 


The  student  may  work  out  the  following  exercise,  using  extended 
auxiliaries  in  the  soprano  wherever  possible,  as  indicated  in  the  first 
four  measures. 


AUXILIARIES 


143 


280 


i 


f=f 


p 


i=ic 


m 


^ 


5if 


^^^ 


r^  nj 


-pt 


?=f=r 


^ 


J 


^ 


■J — ^ 


^ 


5        -       b7 


fe 


f 


,^ 


^    ^       '^^^^^ 


e^ 


1" 


f- 


1; 


A 


M 


J 


etc. 


f«=^ 


C     r     C 


i.    LJ  r 


r 


b7 


11 


5         4         6 


i 


nr  r  r  r  |i^^ 


1^ 


:^ 


i 


*   ^  *-l^  r  f 


fe# 


* 


4t 


»  * 


I 


Also,  the  same  exercise  with  extended  auxiliaries  in  alternating 
voices,  as  follows: 


144 


CUMULATIVE   HARMONY 


281 


i 


m 


i 


4r*: 


^ 


TW 


^ 


Mi 


-i 


^ 


etc. 


^3 


4-(^- 


ri^ 


From  the  same  germ  set  form  a  continuous  eighth-note  motus, 
first  in  the  bass,  then  in  the  tenor,  alto,  and  soprano  successively, 
utilizing  the  various  embelHshments  thus  far  admitted.  To  the  germ 
set,  notes  may  be  added  in  the  soprano,  only  as  embellishments. 
When  such  embelHshments  are  also  harmony  notes,  they  must  be 
given  due  consideration  as  such  in  the  selection  of  harmony  notes 
for  the  other  voice  parts.  A  separate  staff  for  the  germ  set,  when 
embellishments  are  to  be  employed  in  the  soprano,  is  necessary. 

282 


#5K 


i=^^^ 


0=M^^ 


r-1 


^ 


4^^— ¥ 


If 


J. 


A 


W- 


r    r 

^ 


etc. 


±:Sz 


283 


/i^a 


4  I 1 

2  4-7 

3 


^L^ 


r 


J:    A 


r  ^  *  briH^ 


r 


5-4 


111.  No.  68 
Allegro 


AUXILIARIES  145 

Richard  Wagner,  " Tannhaueser  March" 


(CTb 


y, 


^m 


^^=^ 


fee   J  J  J  >j 


M     ^x>f 


^5S 


^>  ^  » 


(^ 


hA.      /J^Xj 


i 


f 


-i» m 


-<2- 


r 


Wr^  IjJr^ 


:?l=l*t 


:iMf 


^: 


This  may  be  followed  by  a  continuous   sixteenth-note   motus  in 
each  voice  in  succession,  also  in  alternating  voices. 


284 


i 


J 


■i iS»- 


fg 


^ 


r 


Pe 


^ 


J. 


fM'-F-M* 


^^ 


*=i^ 


f-f-^-V: 


5-4 
2 


(F^ 

1 

— «i- 

-J— 

1 

1* 

/L 

J- 

—m— 

-4— 

1 

=j 

% 

^ 

-c — 

etc. 

>- 

1 

>- 

ZJ 

p 

=f=¥= 

-^ 

f  r  r  r  .  ip_u£^^r  r  r  r 


146 


CUMULATIVE   HARMONY 


f$^m 


g    I    ^ 


i 


I 


Combinations  of  various  rhythmic  figures  may  be  formed  in  alter- 
nating voices,  some  examples  of  which  are  given  herewith: 


285 


I'll  Lj  L-d  !  '  '  '  ii !  i-T  Lj  '  '  '  I  I r 

11    0  -  0  p  ^  p  p  0    p  ^  0  0  p  p     \\ 


Also  a  continuous  sixteenth-note  motus  in  two  voices  simultane- 
ously. 


286 


m 


^ 


s^^ 


(^ 


IM= 


*^^ 


-4 P ^ 


:#*: 


-J-* 


^-*-J- 


«^- 


ft^ 


etc. 


s#- 


i^ 


3-:^^_J-^JL 


:^=q»=^^^ 


^^BqS: 


^3 


l-L 


in.  No.  69 


J.  S.  Bach,  "  Choral  Prelude  "  (for  organ ) 


^ I 


Jfft 


H     ^ 


# 


■^n»nT 


:5=*: 


^ 


5lt- 


e3I 


-:3u4   - 


i^ 


m  ^  m 


S 


5 


AUXILIARIES 


147 


0rl    ^     ^^^ 


Additional  exercises  for  similar  treatment  follow. 

287 


3E 


m 


tSH- 


>^I=^ 


i 


:r?        *     1^ 


¥ 


I   r  T 


i 


i 


288 


I?. 


i 


-f^^m 


*   in 


^-^ i- 


tlr-    r  ^ 


— V  -r 


^£ 


:?c:^^ 


?=^ 


-«> ^- 


-• — Ti     •■ 


I 


CHAPTER   XXIV 


INTRODUCTORY  AUXILIARIES 


Auxiliaries  not  preceded  by  the  harmony  note  upon  which  they  de- 
pend occur  frequently  at  the  beginning  of  a  composition  or  phrase, 
and  for  that  reason  are  referred  to  as  introductory  auxiliaries.  An 
introductory  auxiUary  may  be  used  on  the  accented  or  unaccented 
part  of  a  measure  or  beat;  it  may  appear  as  a  grace  note,  in  which 
case  it  is  termed  an  appoggiatura,  or  in  combination  with  other  notes 
may  form  a  turn;  or  it  may  occur  as  an  independent  note  of 
definite  rhythmic  value. 


289 


{^) 


,(0 


-^- 


i 


H^ 


-(^ 


s^ 


-J^^ 


^*r^^T^ 


s 


:«^ 


ty 


{d) 


{e) 


(/) 


At  (a)  it  appears  as  an  introductory  auxiliary  below  the  harmony 
note  G,  on  the  unaccented  part  of  the  beat;  at  (6),  as  an  auxiliary  below 


INTRODUCTORY   AUXILIARIES 


149 


E,  on  the  accented  part  of  the  beat;  at  (c),  as  an  auxiliary  above  E, 
on  the  accented  part  of  the  measure;  at  {d),  in  syncopated  rhythm, 
on  the  unaccented  part  of  the  bar;  at  {e),  as  a  grace  note,  and  at  (/), 
to  aid  in  forming  a  turn  before  the  harmony  note  C.  Work  out  the 
following  germ  set  and  bass  set  using  introductory  auxiliaries. 


290 


m 


(i 


m 


fT-^ 


^ 


r 


^-      J     V 


^ 


a^ 


III 


6         4 
3 


* 


mm 


(1 


r 


J. 


etc 


11 


J  6 

6         4 


m^ 


^ 


^^ 


^ 


p 


=^-*- 


-^ 


-^=^4 


:^^^ 


i^ 


150 


CUMULATIVE   HARMONY 


291 


IE 


*=»= 


f- 


.Li. 


m 


r 


^s 


f^- 


etc. 


Tt 


'S 


-iS^ 


'S^ s^ 


-^ 


— iS* ^zr- 


1^- 


tt6 
4 


6  #6 
4 
3 


7         6 
b       b5 


-^:H?^     ^.      J     J    ir  .  J   !i'^-{?r.    1  J      ! — \ r+^ h H 

^     ^~t 1 — 

6 

r^ ^-+1 ^_H| 1 1-'      '      m      J\^ ^^-\- H 

6         7                     7                   4!44|6|76           1        '^ 

5         tt                                         2       ||3        b     ^      [1^5    4 

b 

111.  No.  70 


MOSKOWSKI 
"  Tarantelle,"  op.  27,  No.  2 


McCoy,  "Prelude  to  The  Hamadryads  " 


Progressive  auxiliaries  are  of  two  kinds:  an  auxiliary  above,  re- 
turning to  a  harmony  note  a  third  or  more  below;  and,  conversely, 
an  auxiliary  below,  returning  to  a  harmony  note  a  third  or  more 
above.  It  may  return  to  a  harmony  note  of  the  same  chord,  or  of 
another. 


INTRODUCTORY    AUXILIARIES 


151 


292 


^ 


^ 


E 


4r- 


r-j  '-^ 


-J—>i- 


^g-^-^ 


g 


j- 


is 


.J-' 


Ui 


J- 


^ 


i 


^ 


?^^ 


a-  r    r 

4  6 

2 


:|i 


The  student  will  have  no  difficulty  in  comprehending  this  embellish- 
ment as  exemplified  in  the  above  example. 

m.  No.  72     Peri,  "  Eurydice  " 


m.  No.  73     Mendelssohn,  "  Quartette  in  A  Minor  " 

/r 


fefe^^^^^^ 


(le^ 


m 


152 


CUMULATIVE    HARMONY 


Accented  passing  notes  and  auxiliaries  are  frequently  longer  than 
the  harmony  notes  to  which  they  belong. 


293 


J 


A 


T 


-r^- 


4- 


r 


Changing  notes  are  formed  by  a  combination  of  two  embellishments 
located  a  diatonic  degree  above  and  a  chromatic  (generally)  degree 
below  a  harmony  note  that  follows. 


294 


(«) 


{f>) 


J=iJ=i 


^ 


J=i 


(O 


{d) 


-»-    J 


^-^ 


-X 


At  (a)  the  changing  notes  are  formed  by  a  combination  of  aux- 
iUaries  below  and  above;  at  (6),  by  a  combination  of  an  extended 
auxiliary  above  and  an  extended  passing  note;  at  (c),  of  a  passing 
note  and  an  extended  auxiHary  above,  and  at  ((/),  by  an  extended 
auxiliary  below  and  an  extended  passing  note. 


m.  No.  74 

A  llegro* 


Spohr,  "  Nonet" 


3^^ 


1^ 


1^ 


^ 


-si- 


-m 


"^ 


\\\ 


-^1r 


^ 


IM 


^ 


\-Az 


^  •  w- 


B^ 


An  anticipation  is  the  use,  in  the  same  voice,  of  a  harmony  note  of 
one  chord  during  the  latter  part  of  the  time  of  the  preceding  chord, 


INTRODUCTORY   AUXILIARIES 


153 


of  which  it  does  not  form  a  part.  It  is  generally  short,  although  it 
may  occupy  a  half  of  the  time  of  the  chord  to  which  it  is  attached. 
It  occurs  in  one,  two,  or  three  voices,  and  may,  in  fact,  involve  the 
entire  chord. 


205 


tm 


i 


±3i 


-TSh 


I^ 


r 


m 


J- 


T- 


in.  No.  75 


^W^ 


Richard  Wagner,  "  Parsifal " 


fff^^^^^^s^ 


^ 


?2:^ 


U^ 


r 


:^ 


±^ 


^ 


)H3: 


^^5>(! 


^ 


±^ 


^?^=tt 


fes= 


bigJ  <g-. 


b^ 


in.  No.  76 


i 


Haendel,   "L'Allegro" 


&^$: 


-TSh 


^s 


#^ 


:1N 


J 


^ 


J.       i 


J 


^ 


izte 


fW=f 


The  student  should  continue  the  use  of  all  embellishments  in  his 
work. 

A  false  relation  is  the  employment  of  a  note  in  one  voice  part,  and 
its  chromatic  alteration  at  the  same  time  or  immediately  following  in 
another  part. 

False  relations  do  not  seem  to  be  objectionable:  when  they  are  pro- 
duced by  embellishments  (a),  when  the  fundamental  of  the  second 
chord  is  a  third  above  or  below  the  first  (b),  and  when  the  note 
and  its  chromatic  alteration  progress  in  opposite  directions  (c). 


154 


296 


CUMULATIVE   HARMONY 

{a)  (3)  (c) 


i 


¥ 


-#— t 


^ 


r^f=t 


i 


-J- 


^ 


3t 


-2=^ 


r 


r 


r        r 

6 

The  following  exercises  should  now  be  worked  out  in  several  keys, 
with  a  continuous  eighth-note  motus  in  alternating  voices,  and  then 
in  individual  voices,  employing  introductory  auxiliaries,  progressive 
auxiliaries,  and  changing  notes. 

The  same  may  be  subsequently  done  with  a  continuous  eighth-  and 
a  continuous  sixteenth-note  motus,  employing  all  preceding  em- 
bellishments. 

207  I  . 

J     ^ 


(a) 


(i) 


{d) 


^ 


<«)  (/) 


w  if  i-- 


T" 

U 


r 


(m 


-J 


\>m    0 


^ 


f 


4(0 
2 


iii 


-^2- 


(^) 


1^ 


(0 


U) 


U)       (^) 


i- 


#^ 


^ 


-A- 


{h) 


r 


:/ 


J — ^'^ 


#6 
4 


INTRODUCTORY  AUXILIARIES 


"^SS 


A^--^r¥r^^^^ 


b#    fi 


i^E^ 


* 


S^ 


^ 


^ 


:2: 


At  (a)  we  have  an  introductory  auxiliary  below;  at  (b),  the  chro- 
matic passing  note  C#  and  the  extended  auxiliary  E,  forming  changing 
notes  on  the  harmony  note  D ;  at  (c) ,  the  harmony  note  C  used  as  a 
progressive  auxiliary  above  the  Bb,  for  motus;  at  (d),  the  retardation 
E  and  the  extended  auxiliary  note  G  forming  changing  notes  on  F; 
at  (e),  (e),  progressive  auxiliaries;  at  (/),  a  passing  note  in  the  tenor, 
for  motus;  at  (g),  the  suspension  D  and  the  extended  auxiliary  B  form- 
ing changing  notes;  at  (h),  a  progressive  auxiliary  in  the  alto;  at  (i), 
the  passing  note  and  extended  auxiliary  for  changing  notes;  at  (y), 
(j),  double  changing  notes  in  the  alto  and  tenor,  moving  in  sixths; 
and  at  (k),  an  introductory  auxiliary  beginning  a  phrase. 

The  following  germ  sets  should  be  worked  out  in  like  manner  in 
several  different  keys. 


298 


* 


^^ 


F-»r+* 


^ 


^ 


^ 


■^a- 


=a= 


$ 


-ft—»- 


g^^tfi^rrif 


^' '  I'  uniHJ 


299 


^ 


^ 


-^-=- 


4f^^f 


1 — r^^ 


i 
g 


^ — ^ 


f       ^ 


^ 


+ 

J 1 1 


I 


156 


300 


i 


CUMULATIVE  HARMONY 


m 


si- 


»§ 


S^S 


:#: 


1* 


M 


i^ 


^=^ 


-^ 


ft        -*- 


is"? 


St 


III 


-fi^ 


i 


-f2- 


i. 


¥ 


f^ 


I 


Double  and  triple  embellishments  in  combination  may  be  used 
with  excellent  effect  in  passages  of  thirds  and  sixths  in  similar  motion, 
and  in  contrasting  passages  moving  alternately  and  together  in  con- 
trary motion.  When  embellishments  occur  thus  in  combination, 
they  should,  as  a  rule,  be  consonant  one  with  another.  Dissonances, 
even  extremely  harsh  ones,  may  appear  singly,  to  be  followed  by  a 
combination  of  more  consonant  intervals,  but  a  series  of  extremely 
dissonant  chords  in  immediate  succession  should  be  avoided. 


in.  No.  77 


Arthur  S.  Sullivan,  "The  Mikado" 
6—5 


At  (a)  are  auxiliaries  above;  at  (b)  auxiliaries  below  and  extended 
passing  note;  at  (c),  retardation;   at  (d),  changing  notes,  extended 


INTRODUCTORY    AUXILIARIES 


157 


auxiliary  below  and  extended  passing  note;  at  (e),  chromatic  passing 
note;  at  (/),  changing  notes;  and  at  (g),  extended  passing  note. 

Occasionally  an  entire  definite  chord  belonging  to  some  related  key 
is  built  up  from  embellishments. 

Special  effort  should  be  directed  toward  acquiring  a  good  writing 
technique  in  this  section  of  the  work.  A  ready  facility  in  four-part 
writing,  with  independently  moving  voices,  constitutes  a  strong 
element  toward  future  success  in  analysis  and  composition. 

301 


:5ti: 


±t 


itEE^tEM 


M 


n 


SZZIM 


:d^ 


^^=^^~ 


X^ 


^-fi 


^ 


? 


^ 


^  ^  ir— -g=^ 


^w^=^- 


^cn==^ 


=t 


g=r=rrrtm 


t 


^^ 


1 1 1 W- ^ 


i 


:*=^ 


?f=^ 


0^-^ 


m 


I? 


i 


302 


M 


m 


j^ 


-4n 


ftz^ 


lE^ 


i(—M 


m 


I  ~^ 


:*.« 


n 


^f^ 


m 


~ 


l\3 


iS8 


CUMULATIVE   HARMONY 


303 


i?^fi^ 

^ 

"T^ 

-4- 

•   ^ 

4— 

-^ 

< 

— 3— 

-f-f 

-*- 
— 1 — 

— 

etc. 

\'^bft- 

-n- 



— 1 — 

^ 

1        P 

The  next  step  will  be  the  further  utilization  of  a  germ  set  as  a  basis 
for  the  formation  of  a  melody  with  piano  accompaniment. 

In  these  exercises  four  staves  should  be  used  in  score.  The  first 
or  upper  staff  is  to  be  occupied  by  the  given  germ  set,  the  second  by 
the  completed  melody,  while  the  third  and  fourth,  in  brace,  are  to 
be  used  for  the  piano  accompaniment. 

Harmonize  the  germ  set  in  accordance  with  the  rules  for  harmoni- 
zation of  melodies,  placing  the  chords  in  four  voice  parts  on  the  two 
lower  staves  in  accompaniment  form  as  heretofore.  Care  should  be 
exercised,  in  constructing  the  chords  for  the  accompaniment,  toward 
correct  voice  progressions  and  other  established  laws. 

In  the  following  exercises  each  chord  should  have  a  duration  of  a 
half  or  whole  bar.  Embellishments  are  to  be  used  wherever  necessary 
in  the  construction  of  a  plain,  broad  melody  in  song  style,  employing 
only  half  notes,  dotted  half  notes,  quarters,  dotted  quarters,  eighths, 
and  the  combined  dotted  eighth  and  sixteenth  notes  when  the  exer- 
cise is  in  common  time.  In  g  or  §  time,  series  of  sixteenth  notes  are 
admitted.  Rests  may  be  used  wherever  they  are  considered  ad- 
vantageous. The  time  value  of  germ  notes  may  be  shortened  or 
lengthened  when  admitted  by  the  harmonic  requirements. 

The  harmonization  in  the  accompaniment  must  be  so  constructed 
that  the  given  germ  notes  will  consist  only  of  duplicates  in  unison 
or  octave  of  the  notes  comprising  the  three  upper  voices  of  the 
chords  so  employed.  The  harmonic  content  of  the  accompaniment 
thus  becomes  the  substratum  of  the  melody,  as  the  melody  forms  a 
superstructure  to  the  harmony. 


INTRODUCTORY   AUXILIARIES 


159 


304 


^ 


iia 


g 


-^        #- 


if^iS^ 


^M 


^ 


it 


SS=is 


a 


y- 


-iS'-r- 


fci: 


^ 


y- 


!        I        I 


3 


^J='^ 


^ 


^^"^"^3 


m 


-^ 


i*^ 


^. 


i 


tt 


^ 


^^e 


^ 


i 


fct^ 


?2=lt 


£ 


#^  •^^-A 


bl^^ 


^ 


•  fir-  r- 


3 


i6o 

305 


CUMULATIVE   HARMONY 


^jf-r^ 


3e 


^ 


^la^E^^yc^ 


jffi- 


w 


?p? 


1=^3? 


m 


;e 


i^^ 


These  exercises  should  be  worked  out  in  similar  manner,  with 
different  melody  and  form  of  accompaniment,  after  which  they 
should  receive  new  treatment  for  piano  solo.  Additional  germ  sets 
are  here  appended,  also  other  suggestions  for  accompaniment. 


306 


^ 


m 


fe= 


■%-^ 


n  h             "*■ 

h""       * 

U  D    a ^ 

— •■ 1 

m 0— 

^         t^^     1    1 m 



-G> s 

-f^ — f- — r~ 

-r 

1 — 

— 1 — H — T — * 

1 — 

^K           ' 

1 

1 

J                               ' 

^ 


^ 


3#       r 


i^ 


^^ 


307 


±9= 


i 


3 — h-J,-J. 


etc 


IS 


SH^ 


^ 


b7 


Ste 


(^ 


a 


etc. 


INTRODUCTORY   AUXILIARIES 


i6i 


308 


1^4  J  J  f-j-.>— ^-ji^ — r  r  \r — [¥  r  r  1 

-§M-^--^ — 1 — i — ^ ^  1   f  4 — 1 — ^ 

t»     rt 


^^ 


^^^ 


« 


£ 


^ 


^ 


ni.  No.  78 


Wagner,  " Tannhaeuser  March" 


?>^^: 


-jtim 


gg 


i 


-s>- 


? 


^=^ 


lAs 


p 


^;;3s 


ssft 


wm 


-(S>- — *- 

f 


■W  ^^,# 


IE 


4 


4 


j-.j-4-:^.a 


-=^=t 


J 1 


^      ^ 


:i 


g-    X 


r 


»-..i# 


CHAPTER  XXV 
THE  DOMINANT  NINTH   CHORD 

To  the  D^  chord,  the  9th  may  be  added,  thus  forming  the  chord 

of  the  Dominant  ninth  [D^],  which  must  consist  of  a  major  triad,  a 

9 

minor  seventh,  and  a  major  or  minor  ninth,  figured  5  or  9. 

3 

309 


i 


izsi- 


-g- 


b9 


As  the  D^  chord  contains  five  different  notes,  one,  usually  the  5  th 
or  the  fundamental,  is  omitted  in  four-part  harmony. 


310 


:(]2)s=(l2)g: 


7)) 


As  this  chord  with  the  fundamental  omitted  requires  special  treat- 
ment, it  will  be  discussed  at  length  later  on,  consideration  being  given, 
for  the  present,  only  to  the  chord  with  the  fundamental  included. 

When  the  5th  is  included,  the  7th  is  usually  omitted,  although  at 
times  the  3d  is  omitted  instead.    . 

When  the  5th  is  present  and  is  located  below  the  9th,  it  should  re- 
solve upward  to  the  T^,  which  may  be  doubled  in  the  resolution  to 
the  T  chord.  This  is  in  order  to  avoid  the  faulty  parallel  5ths  that 
would  result  were  the  D^  to  resolve  to  the  T*. 

162 


THE  DOMINANT   NINTH   CHORD 


163 


311 


allowed  allowed 


3 


4 


-5*- 


While  the  D"  chord  positively  determines  the  identity  of  a  tonality, 
it  does  not,  owing  to  its  similarity  in  the  major  and  minor  modes, 
definitely  indicate  its  gender.  On  the  other  hand,  the  D^  chord  is 
used  in  two  distinct  forms,  dependent  upon  the  gender  of  the  key 
from  which  it  is  derived,  the  9th  being  a  major  interval  in  the  major 
mode  (major  D^  chord),  and  a  minor  interval  in  the  minor  keys 
(minor  D^  chord). 


312 


(«) 


(*) 


i 


% 


9  9 

A 

At  (a)  the  chord  of  the  D^  in  the  key  of  C  contains  a  major  9th,  A, 
and  at  (6),  in  the  key  of  a,  the  9th,  F,  of  the  D  chord  is  a  minor  interval. 

As  in  the  case  of  the  D^  chord,  the  D^  chord  resolves  to  the  T  chord. 

The  D»  resolves  to  the  T%  the  D^  D^  and  D^  resolving  as  in  the  D' 
chord. 

313 


5 


(3) 
8 


3  8 


-«5»- 


When  possible,  the  9th  should  be  prepared;  otherwise  it  should  be 
approached  from  below. 

The  D^  occasionally  resolves  by  ascending  to  the  T*  when  it  occurs 
in  the  soprano. 


164 


CUMULATIVE    HARMONY 


314 


3 


hS2- 


111.  No.  79 


Debussy,  "  Pelleas  et  Melisande  " 


t=^ 


g^l 


As  this  chord  is  composed  of  five  different  notes,  it  is  subject  to 
four  inversions.  Of  these  the  first  and  third  are  most  effective;  the 
second  is  rarely  used,  owing  to  its  harshness,  which  is  due  to  the 
omission  of  the  7  th  (made  necessary  by  the  use  of  the  5  th) ;  the  fourth 
inversion  is  not  considered  available,  except  when  the  9th,  as  the 
actual  bass,  is  prepared  by  being  heard  in  the  same  voice  part  as  a 
harmony  note  of  the  preceding  chord. 


THE    DOMINANT    NINTH    CHORD 


^6S 


315 


(^) 


(*) 


(O 


(d) 


i 


fe^ 


-?sf- 


T 


-6h- 


w 


T    r 


I 


4- 


-zi- 


£ 


=^==f 


£ 


-^=i- 


7  4  6  5  6  |[4  7  6 

6  3  4  [[3  6  4 

2  2 

At  (a)  is  an  example  of  the  first  inversion,  at  (6)  of  the  third,  and 
at  {c)  of  the  second  inversion.     The  harshness  and  ambiguity  of  this 
position  of  the  chord,  due  to  the  omission  of  the  7th,  may  be  readily 
perceived;  at  {d)  the  9th  is  prepared  as  the  3d  in  the   ||S  chord, 
m.  No.  80  Sullivan,  "  St.  Edmund  " 


tf 


I 


=3=^ 


f-r^ 


Ifi 


-^- 


II'  679 

5 

The  9th  is  most  effective  in  the  soprano.  This  suggests  an 
additional  rule  for  harmonization  of  melodies. 

When  the  sixth  of  the  scale  is  followed  by  the  fiith,  the  sixth  may 
be  harmonized  with  the  Dominant.  This  will  be  easily  recognized 
as  the  D*  resolving  to  the  T%  as  at  {a). 

The  second  choice  for  use  of  the  9th  is  in  the  tenor.  It  should 
never  appear  a  second  above  the  fundamental,  as  its  resolution  would 
thus  be  anticipated;  for  that  reason  the  fundamental  should  never 
appear  within  an  octave  below  the  9th. 

316 

not  good 


good 


r 
-1 


■fr 


^ 


r 


1^ 


i66 


CUMULATIVE   HARMONY 


As  in  other  chords,  the  position  of  the  various  notes  of  the  D^ 
chord  may  be  transferred  from  one  voice  part  to  another  during  the 
life  of  the  chord,  the  D^  resolving  to  the  T^  in  the  part  where  it  last 
appears,  as  at  (a)  (a)  below;  or  when  the  D^  progresses  by  skip  it 
may  pass  entirely  from  the  chord  without  losing  its  identity  as  a 
note  of  harmony  (b). 

317 


^: 


f 

(a) 


J 


(a) 


r 


(*) 


-f^ 


T 


The  9th  frequently  occurs  as  an  embellishment  above  the  D^  or 
below  the  D^  in  the  D^  chord,  to  which  notes  of  harmony  it  pro- 
gresses before  the  resolution  to  the  T  chord. 

318 


-25^- 


r 


(a) 


-^^ 


-(^ 


-f^ 


At  (a)  A  is  introduced  as  an  auxiliary  above  the  D^,  G;  and  at  {b) 
it  appears  as  an  extended  auxiliary  below  the  D^,  B.  This  must  not 
be  mistaken  by  the  student  for  a  D®  chord,  which  it  temporarily  re- 
sembles in  appearance  and  quality. 

in.  No.  81  Debussy,  "  Arabesque  I  " 

Tempo  rubato 


THE   DOMINANT   NINTH   CHORD 


167 


lU.  No.  82 


^ 


Clayton  Johns,  "  The  Barefoot  Boy  " 


^m 


K 


^^3 


^ 


^ 


-^ — wf — #- 


^1^ 


f=f=t 


^?t=|S 


-r  -r  T-  f 


I*    k    I* 


To  aid  the  student  in  understanding  the  distinction  between  a 
D'  chord  with  embellishments  formed  by  the  aid  of  the  9th  and  the 
D'  chord  proper,  let  it  be  understood  that: 

When  the  9th  progresses  by  degree,  either  upward  or  downward, 
thus  disappearing  from  the  D  chord  before  the  resolution  to  the 
T  chord,  it  must  be  considered  an  embellishment  and  not  an  integral 
part  of  the  harmony. 

If  it  resolves  directly  to  the  T^,  or,  progressing  to  a  difTerent  note 
of  the  chord,  it  resolves  from  that  note  to  the  T^,  or,  in  progressing  by 
skip  to  another  jiote  of  the  chord,  it  disappears  entirely,  leaving  only  a 
D^  chord  to. resolve  to  the  T  chord,  it  is  an  essential  member  of  the 
Dominant  harmony  as  an  interval  of  a  9th. 


m.  No.  83 


Haydn,  "  Quartette" in  G  " 


J    ,"  J  ^  J.     I 

i^   V  -*-  —    —    =       — 


#ftf^ 


^ 


± 


=^ 


^ 


isz: 


^si; 


J'-^ 


m.  No.  84 


Massenet,  "  Elegie  " 


i68 


CUMULATIVE    HARMONY 


^ 


M 


F? 


f    T   U 


fer 


s 


The  D^  is  occasionally  ornamentally  resolved  by  the  interpolation 
of  the  D^  (in  the  form  of  an  embellishment)  before  its  resolution  to 
the  T^ 

In  such  cases  the  quality  of  the  D^  as  a  harmony  note  is  not  lost, 
as  it  is  when  the  succeeding  D^  is  attended  by  its  compulsory  resolu- 
tion to  the  T8. 

319 


f 


r 


A  chord  of  the  D^  may  progress  to  a  D^  chord. 

320 


1 


Harmonize  the  following,  using  D^  chords  wherever  practicable,  in 
accordance  with  the  directions  given  above, 

321  +  I 


^ 


sl- 


Bi 


-(S2_ 


m\ 


i=i 


4- 


■^ 


j- 


j 


-(^ 


-r 


THE   DOMINANT   NINTH    CHORD 


169 


=t=^ 


t^ 


f2 G>- 


-a fa- 


£ 


-<2 ^ 


:)te: 


i 


? 


322 


s 


J.    J  J 


s 


r^f=f 


ft-g-^ 


-#— •- 


f^=5= 


yn 


etc 


li 


jt  V 


J" 


s 


6       6  3       6 

4  2 


6       7       6^-  17       6 

6       4       ® 


NJii£;rcirKm^-^r:;iLrrrgirT 


CHAPTER  XXVI 


THE   ABBREVIATED  DOMINANT  NINTH   CHORD   D)) 

With  the  omission  oi  the  fundamental  in  the  chord  of  the  D^  the 
four  remaining  notes  present  a  series  of  thirds  in  the  form  of  a  chord 
of  the  seventh  on  the  subtonic  as  a  leading  tone.  The  subtonic  is 
here  considered  as  the  nominal  fundamental,  the  real  fundamental 
being,  of  course,  the  Dominant,  which  is  also  the  primary  note  of 
the  chord.  The  symbol  D))  will  be  used  with  the  figuring  for  identi- 
fication in  analysis. 

323 


-^ 


-s^ 


J J- 


7))  7)) 


7)) 


The  treatment  of  the  abbreviated  form  of  the  D^  chord  is  subject 
to  the  following  conditions: 

I.  No  member  of  the  chord  may  be  doubled  or  omitted. 

II.  The  D^  may  not  progress  to  the  D^  or  D^  before  the  resolution 
of  the  D  chord  without  losing  its  identity  as  a  note  of  harmony. 
With  such  progressions  the  chord  will  be  recognized  as  a  D^  chord 
with  an  embellishment,  as  heretofore  described. 

324 


r 

(a) 


^ 


'-I5'- 
I 

I 


-(S2- 


^^ 


K6 
5 


4 
3 

170 


THE   ABBREVIATED   DOMINANT  NINTH   CHORD 


171 


At  (a)  the  interval  in  question  is  shown  as  a  form  of  suspension; 
at  (b)  as  an  auxiliary  above  the  harmony  note,  G;  and  at  (c)  as  an 
extended  auxiliary  below  the  harmony  note,  B. 

III.  This  chord  may  be  freely  used  without  preparation  in  all  in- 
versions except,  perhaps,  the  last  one,  in  which  the  D^,  in  the  bass, 
is  preferably  (not  necessarily)  prepared,  as  at  (a)  below. 


325 


(a) 


C^)         (0 


ijm 


i 


T f r 

i      -J-      J 


1:2: 


D) 


t)) 


This  inversion,  although  prepared,  is  not  as  satisfactory  as  the 
others,  owing  particularly  to  the  somewhat  objectionable  4  chord 
which  JoUows  as  the  resolution  (b).  This  unsatisfactory  condition 
may  be  overcome,  in  a  measure,  by  a  diatonic  progression  downward 
through  a  succeeding  chord,  as  at  (c). 

The  various  positions  of  this  chord  may  be  described  as  follows: 


326 


i 


(a)  {b)  (c 

I      J      J 


(rf) 


W^ 


A 


y^d^mm 


7))  5))  3))  2)) 


The  fundamental  position  (D^  in  the  bass)  is  figured  7)) ;  the  first 
inversion  (D^  in  the  bass)  is  figured  |));  the  second  inversion  (D^  in 
the  bass)  is  figured  3));  the  third  inversion  (D^  in  the  bass)  is  figured 


i)). 


The  resolution  of  the  various  members  of  the  chord  is  the  same  as 
when  the  real  fundamental  is  included. 

The  D^,  except  when  in  the  bass,  may  resolve  upward  or  downward 
to  the  T^ 


172 


CUMULATIVE   HARMONY 


327 


i 


c^ 


T 


-z^ 


J: 


7))  7)) 

The  D^  with  the  D^  above  it  is  at  times  resolved  to  the  T*  in  the 
minor  keys,  as  the  first  of  the  resultant  parallel  fifths  is  a  diminished 
interval. 

328      i 


^ 


J. 


^ 


7)) 

The  student  is  advised,  however,  to  avoid  such  progressions,  at 
least  for  the  present,  preferably  doubling  the  T^  in  the  resolution. 


329 

1 

/^^•         1       ' 

1 

^ 

1         1 

\fi)'{  I 

^ 

A 

m            '            ' 

-fS 

~ 

^ 

J     1 

Ki^y  J    f^       \        \ 

^ 

» 

1        1       r 

W     uJ         {         1 

1 

^ 

L| 1 L^ 

-* 4-J 

4U      6        |J_7  7)) 


D) 


•D) 


'T\]l    t 


))  '  .1)) 


m 


3 


:#»t 


-z)- 


V)) 


1=^ 


))•  E 


6       b7)) 
4 


7)) 


)) 


^ 


117 


))    '    ^t)) 


7)) 


m.  No.  85 


JOHANN  LuDWiG  Krebs,  "  Bourr^e,"  from  Suite 


r  T    r  r 


rn 


7» 


7)) 


5) 


THE   ABBREVIATED    DOMINANT   NINTH    CHORD      173 

m.  No.  86  MOSCHELES,  "  Study,"  op.  70,  No.  4 


pg^^ 


^^^^ 


--¥ 


^t3=J:3)j|*=F^ 


m 


m 


'-^ — 9 


^=5: 


tj7)) 


.9) 


?^ra3 


!^))   ''»  IJ))  ^ 


The  resolution  of  the  D^  to  the  T^  suggests  an  additional  rule  for 
modulation  in  a  given  melody: 

When  the  indicated  (+)  note  of  modulation  descends  a  step,  or  a 
half  step,  it  may  go  to  the  fifth  of  the  scale  in  the  new  key.  The 
modulation  must  be,  of  course,  to  a  directly  related  key.  The  note  of 
modulation  will  here  be,  obviously,  the  D^  (major  or  minor),  resolv- 
ing to  the  T^. 

330 


S=S=^ 


s^m^- 


S 


T— W  f— 7# 


^^- 


J  n  rz  n- 


u  w  lj 


■^ 


t  * 


=))      '»      t)) '  «=■')  ^  1)) 


E 


^^S 


-^  .0 


etc. 


-^ *- 


-^ *- 


n))  ^  ,J)) !  -J))  ^  D) ' 


S 


=itF 


^^ 


prffTT^j^^tci^ta^ 


174 


CUMULATIVE   HARMONY 


As  may  be  seen,  the  alternate  notes  of  the  melody  in  the  exercise 
above  should  receive  D))  chords.  It  should  be  transposed  to  other 
keys,  and  harmonized  both  with  fundamentals  present  and  omitted. 

m.  No.  87  Grieg,  "  Gavotte,"  op.  40,  No.  3 

* 

4 


m 


^4^ 


^ 


m 


-X- 


-^ * •- 


% 


T 


— I 1 ^- • r:) «- 


*  The  D^  here  resolves  to  the  T^  in  order  not  to  anticipate  the  subsequent  T'  in 
the  melody. 

in.  No.  88    Schubert 

"  Grand  Duo,"  op.  140 


JP 


j-^ 


i^. 


1 


r 
J. 


-^- 


7)) 


)) 


The  minor  D))  chord,  commonly  known  as  the  diminished  7th 
chord,  has  long  held  an  important  place  in  the  harmonic  structures 
of  all  forms  of  composition.  It  contains  a  minor  3d,  diminished 
5th,  and  diminished  7th,  and  appears  as  a  series  of  minor  3ds  from 
the  nominal  fundamental. 

The  four  notes  constituting  it,  therefore,  stand  as  points  dividing 
the  octave  into  segments,  distant  a  step  and  a  half  apart.  Mem- 
bers of  the  chord  frequently  occur  with  enharmonically  changed 
notation  for  purposes  of  simplification  and  for  improved  voice  lead- 
ing. For  analysis  the  student  should  mentally  arrange  the  chord  in 
a  series  of  thirds  and  then  identify  the  major  third  below  the  lowest 
note  as  the  fundamental  Dominant.  Altered  notation  may  gen- 
erally be  corrected  by  consideration  toward  directly  related  keys. 
This  chord  is  frequently  used  in  the  major  mode. 

Harmonize  the  following  exercise,  using  D^  and  D))  chords  where 
feasible. 


THE    ABBREVIATED    DOMINANT    NINTH    CHORD      175 


881 


(a) 


m 


±^fat^ 


(«)         (a)       (a) 


^^ 


i 


a^ 


0  ^  i 


-u 


m 


j_i 


^Tj^; 


«^ 


^ 


r^^ 


tT^^^ 


?E=^ 


.    6     6        '))       «1 


:)) 


6      6         5-4 


6      6 


Z^ 


4      4 


'))'  f)) 


r*o) 


i 


^P  r  it  r¥^ 


SE 


^ 


^3 


j=^  r  tj^i^^=£fir^^j^?^^ 


S 


:il*= 


-^— rtr    ^  1-^ 


:?=^ 


^ — ^ 


:^=^ 


i 


s 


-^— ^ 


£1^1^ 


!      i      '      I   I 


hS"^ 


I     I     I 


:tii^ 


At  (a)  (a)  the  diminished  seventh  chord  appears 

111.  No.  89 

Chopin, 


Chopin,  "Etude,"  op.  10,  No.  3 


\p^w^^^^^m. 


#- 


^;j  «^^     *.))  ft.))  |.))  b5))  .^^ 


As  an  additional  factor  in  the  harmonization  of  melodies,  following 
the  rule  for  forming  a  D''  chord  with  a  passing  modulation  when  the 


176 


CUMULATIVE    HARMONY 


primary  note  or  fundamental  ascends  a  fourth,  the  student  may  now 
include  the  D^,  which  may  be  applied  with  or  without  the  fundamental. 

(a)  {b)         {c)  {d)  {e) 


332 


.r-TJ I 


P       m 


^ 


=r 


J 


115^^1 


r^  .j-i  /e  ^ 


^ 


^   ^Jn:J7 


||6        7 
ijs        6 


{g)         (/O 


m 


~0     ^ 


* 


'^^- 


^ 


F#^ 

=^ 

rte^ 

f*- 

«    ^ 

^ 

-^— 

Y 

-^ 

+ 

^ 

=pq 

a 

t^fc= 

' 

"k 

-Wk 

' 

' 

-^ — 

-^ 

:^z 

1 

At  (a)  the  primary  note  G  ascends  a  fourth,  inviting  a  passing 
modulation,  which  is  accomplished  by  adding  the  minor  7th,  Fit. 
A  DS  is  thus  formed  which  resolves  at  (6)  to  the  |  S  chord.  At  (c) 
the  D^  resolves  directly  to  the  T  triad.  At  {£)  the  primary  note  G 
ascends  a  fourth  to  the  primary  note  C,  involving  a  passing  modula- 
tion [DS]  through  the  use  of  the  D^  chord  on  G.  At  (e),  where  the 
fundamental  A  ascends  a  fourth  to  the  fundamental  D,  the  forma- 
tion of  a  D^  chord  is  accomplished  by  the  elevation  of  C  and  the 
inclusion  of  the  9th,  B,  effecting  a  passing  modulation  [DD].  At  (/) 
the  diminished  7th  chord  is  introduced  in  the  major  key.     At  (g) 


THE    ABBREVIATED    DOMINANT   NINTH   CHORD 


177 


{h)  the  D))  chord  is  again  employed  to  good  effect.  The  student 
should  complete  the  exercise  in  similar  manner,  then  work  it  out  in 
several  transposed  keys. 

In  the  following  examples  the  D^  chord  is  to  be  worked  out,  both 
by  omitting  and  by  employing  the  fundamental,  according  to  the 
judgment  and  taste  of  the  s.tudent. 

Effort  should  be  exercised  toward  the  introduction  of  passing 
modulations  (using  the  D^)  on  the  basis  of  the  primary  note  or  funda- 
mental ascending  a  fourth  when  such  opportunities  are  presented. 
This  includes  the  chord  progressions  of  T  to  S,  [S,  or  [[S,  and  of  yS 
to  Dominant. 


333 


ij 


a 


it 


^ 


i"=r 


9^ 


JZ^ 


u 


^ 


^ 


^ 


te 


^ 


^))  :   3)) 


\>^))    \L 


6  4 

5     -    M 


z 


^ 


i 


^ 


s      • 


d     •- 


£ 


r^ 


5)) 


9^ 


6  4 

3 


f=c 


^       m 


L^ 


A 
^ 


r 


IL' 


1  ^I 


5) 


178 


CUMULATIVE   HARMONY 


334 


t 


A 


s 


!=»!: 


f=f=r 


^^B: 


=i^ 


■■^^^ 


V   ^ 


^ 


:&^ 


b7b7))  |5_      6 


0) 


)) 


=«F 


7)) 


-J .4- 


i^ 


:«^ 


^r=^r^=^ 


=^=«F 


f 


.^ll^ 


J- 


^=12^ 0-- 


S4 
2 


4)) 


)) 


4\\  |t>6    ;|4 


0) 


1|2//  l_4     ||3 


:ii 


^* 0-- 


:^m-- 


t^-- 


-# 0- 


--^ 


+ 
-# s> 


-^ 


r='   I   P 


FF 


£ 


^ifF 


-* — ^- 


h5^- 


Melodies  should  be  constructed  from  the  following  germ  sets, 
using  the  D^  and  D^  chords  where  they  may  seem  most  effective. 
They  may  be  worked  out,  for  solo  with  accompaniment,  and  for 
piano  solo. 


THE   ABBREVIATED    DOMINANT    NINTH   CHORD       179 


335 


m 


i     r 


m 


S 


S 


lE 


:?q» 


P^ 


s= 


^ 


^)) 


-S?. 


M^ 


?P^ 


^^^ 


9t^ 


^ 


.^ 


+ 


*=fe 


a 


>- 


m 


^^^^^f 


336        A 
Key  of  c 


Wi 


|ii^ 


m- 


^ 


feBii 


S±^ 


zzz 


1^ 


^^ 


^ 


£^ 


*e)K.f: 


f^¥- 


"» h.pr. 


S 


s 


^^ 


i 


^ 


fe^=f= 


^  •    m 


fcuci 


f^ 


l&§ 


P^ 


rnr  r^ 


CUMULATIVE    HARMONY 


'f=r=r-- 


^^— ^ 


^=f^^=^^hi 


S 


-^^-r^ 


'^^m 


;»-(-^-4 


=t^r^ 


Beginning  with  the  harmonization  of  melodies,  the  work  of  the 
student  has  been  conducted,  generally,  under  a  given  melody  or 
germ  set.  From  this  practice,  the.  ability  to  develop  good  melodies, 
it  is  confidently  hoped,  has  been  assiduously  cultivated.  The  forma- 
tion of  melodies  with  full  knowledge  of,  and  due  consideration  for, 
their  germ  content  is  of  the  utmost  importance  toward  the  attain- 
ment of  success  in  melodic  composition  within  the  bounds  of  such 
limitations  as  circumstances  may  demand,  as  well  as  to  a  better  ap- 
preciation of  the  same  in  the  work  of  others. 

The  plan  of  harmonization  and  melody  formation  over  a  given  bass 
set,  must,  however,  be  considered  of  equal  importance,  and  should 
be  diligently  pursued  throughout  the  work. 

While,  heretofore,  melodies  have  been  evolved  over  a  given  bass  set, 
using  duplications  from  the  upper  three  voice  parts  of  the  harmonic 
structure,  the  student  may  now  enlist  the  employment  of  embellish- 
ments upon  the  harmony  notes  as  may  be  desired  in  such  melody 
construction. 

In  the  following  exercise  the  student  should  fill  out  the  three  upper 
voice  parts,  as  indicated  by  the  symbolized  figuring  of  the  given  bass, 
in  the  same  manner  as  heretofore. 


THE    ABBREVIATED    DOMINANT    NINTH    CHORD      i8i 


888 


m 


rn ,  J   ^ 


m 


^ 


s 


t>j 


1 

^ 


-X 


i^ 


1?^ 


^ 


^ 


b7)) 


^     \ 


9) 


P 


^ 


-^ 


tlF 


-6^ 


^ 


ss 


-J. 


J i- 


etc. 


:«^ 


>^ 


^rj)) 


6 


11 


N#4 
2 


14     6   5    ":    -4      ^^tt*     ^ 


6-7))   4 


«2))       ^     [13         4 


4         6 
2 


1'7)) 


[b.       ^6 


r.))  t 


m. 


i 


1^ 


-TS*- 


6        b7 

4 


4  6  [6^         6 

2         b5  4 


7)) 


D) 


S6\\     6        7))      6 


\    D) 


^ 


4U      6S6\\    li  6         7 


:i^ 


6  7 

4  if 


He 

5 


b7))    [1 


))  'Je)) 


Also  work  out  the  above  exercise  with  an  eighth-note  motus  in  the 
soprano,  the  alto,  and  the  tenor,  in  turn  and  alternately.  In  like 
manner  work  out  a  sixteenth-note  motus  and  various  other  rhythmic 
figures. 


I«2 


CUMULATIVE   HARMONY 


339 


-^-ii. 


r 


(i 


J- 


i*. 


etc, 


4= 


i*: 


^ 


1,7))         [5_      7 


^   0) 


340 


"S^- 


r  » r  T=j^gsj» 


r — t 


(^iife 


-i 


»-* 


J- 


-<2iL- 


=^ 


l}7)) 


t 


Harmonize  the  same  bass  set  for  accompaniments,  in  various 
forms,  from  which  melodies  are  to  be  constructed,  employing  harmony 
notes  from  the  three  upper  voices  and  their  embellishments. 


341 


ii^ 


— I ' — ^ 1 r- 

3       ^*      ^-     ^      ¥- 


An  additional  exercise  is  appended  for  similar  treatment. 


THE    ABBREVIATED    DOMINANT    NINTH    CHORD      183 


842 


fe 


#''  ^  i  t^ 


i 


s 


i 


1         j:       4-=^ 


^s^^ 


!SS 


=t 


-z>- 


"K 


5)) 


i 


^3^ 


3e 


■*--* 


^^ 


J 


^ 


b   1       I 


«k     ^ 


etc. 


(1 


■)) 


-iN= 


^ 


^ 


t«^ 


-^5^ ^ 


b7)) 


')) 


6  7 


II! 


7)) 


I 


:J^==& 


"S^ 


-)i?- 


3))  ^  : 


6  4  6        [[7 

2 


6  6 

5  4 

b 


111.  No.  90 


Bach-Gounod,  "  Ave  Maria" 


^- 


:^^^:^ 


Ma  - 


^ 


#    !  J  ^ 


^ 


^ 


1 84 


CUMULATIVE   HARMONY 


k-^ 


5=5=^ 


-4=? 


#i -_ 


^ 


-(2- 


gra 


f^^ 


'V- 


i 


S: 


ti-  a 


pie 


Do 


1^ 


r^ 


— ii — •- — t* — 


ffi 


mi-nus 


^1 ^ 


^ 


CHAPTER  XXVII 
IMITATION 

With  the  introduction  of  embellishments  the  student  has  been 
brought  directly  to  the  practice  of  certain  phases  of  counterpoint. 

Counterpoint  is  the  art  of  combining  separate  melodies  in  such 
manner  as  to  conform  to  the  laws  of  harmony. 

By  separate  melodies  is  meant  two  or  more  sets  of  single-note 
successions  that  differ  melodically  or  rhythmically  from  each  other. 
If  in  placing  these  melodies  in  immediate  association  (to  be  sounded 
at  the  same  time)  the  laws  of  harmony  have  been  complied  with,  the 
parts  will  necessarily  appear  in  satisfactory  harmonic  agreement; 
ideal  contrapuntal  results  are  not  obtained,  however,  without  due 
consideration  for  individual  melodic  succession  in  each  part. 

In  the  following  example  a  single-note  succession  of  five  notes, 
called  a  subject  or  motive,  is  presented  at  different  locations  in  the 
scale;  as  the  rhythmic  and  melodic  figure  in  each  case  is  identical, 
they  are  to  be  considered  as  melodic  duplications. 

343 


^  I  xs- — • 


^ 


I 


-^-^ 


•    9t    • 


If  we  were  to  combine  the  first  statement  of  the  subject  with  either 
of  the  others  in  immediate  association,  the  result  would  be  harmoni- 
cally satisfactory. 


344 


^0=S-g-*. 


J: 


■721 


^ 


I 


r-^rr 


The  effect  of  such  combination  is  the  delivery  of  the  subject  in  the 

soprano  with  a  duplicate  of  the  subject  serving  as  a  harmonic  support 

in  a  second  voice,  but  the  element  of  rhythmic  or  melodic  independence 

is  entirely  lacking. 

i8s 


1 86 


CUMULATIVE   HARMONY 


If,  however,  the  melodic  succession  of  the  contrasting  melody  is 
distinctly  at  variance  with  the  subject,  its  individuality  directly  be- 
comes apparent. 


345 


i 


A 


J=J=^ 


A 


ESE^ 


;0 


^— » 


r 


r^ 


r 


r-rr 


Here  the  two  tone  successions  are  melodically  at  variance,  and  the 
independent  melodic  effect  is  evident. 

Now  cause  the  contrasting  melody  to  appear  in  a  different  rhythmic 
succession,  thus: 


346 


i 


J- 


ri 


^^i^ 


i 


W- 


=p=i== 


r  r  rr 


r-r^ 


p  ^ 

^ 


and  the  effect  of  independence  becomes  at  once  more  pronounced. 

As  will  be  perceived,  rhythmic  variance  is  a  most  effective  medium 
toward  independence  and  individuality  of  voice  parts.  The  same 
medium  is  equally  necessary  in  three  or  more  parts. 


347 

=^=H 

-^ 

^ 

-a-. — 

=j— 

Y^=^=^ 

IF 

1 

One  of  the  most  important  divisions  of  contrapuntal  writing  is 
that  of  Imitation. 

Imitation  is  a  musical  device  consisting  of  the  announcement  of  a 
phrase  in  one  voice  part  and  its  immediate  recurrence  in  another. 

An  imitation  may  be  a  repetition  of  a  complete  subject  or  frag- 
ments of  its  stronger  sections. 

In  the  imitation  the  rhythmic  figure  is  required  to  be  an  exact 
reproduction  of  the  rhythmic  figure  in  the  subject.  The  melodic 
form  must  agree  with  the  following  conditions: 


IMITATION  187. 

The  melodic  figure  in  the  imitation  ascends  and  descends  as  in  the 
subject.  Where  the  progression  is  by  degree  in  the  subject,  it  should 
proceed  similarly  in  the  imitation.  Where  it  progresses  by  skip  in 
the  subject,  it  must  also  proceed  by  skip  in  the  imitation,  but  the 
skip  may  be  greater  or  less  than  in  the  subject  when  made  necessary 
by  harmonic  limitations. 

It  may  be  understood  that  chromatic  exactitude  in  the  imitation 
is  not  required ;  where  in  the  subject  a  progression  of  a  major  interval 
occurs,  a  minor  may  occur  in  the  imitation;  for  a  diatonic  progression 
a  chromatic  may  be  used,  and  so  on. 

A  skip  of  a  third  in  the  subject  may  not  be  made  a  degree  less  in 
the  imitation,  as  it  would  thereby  become  a  progression  by  degree. 

It  is  at  all  times  desirable  that  the  melodic  figure  in  the  imitation 
appear  as  nearly  like  that  in  the  subject  as  the  harmonic  limitations 
will  permit. 

Imitation  in  Two  Voices 

Using  the  notes  of  the  given  germ  set  and  such  embellishments  as 
may  be  desired,  form  a  melodious  subject  in  the  first  measure  of  the 
following  exercise.  This  is  to  be  succeeded  in  the  second  measure 
by  an  imitation  of  the  subject  in  the  second  voice,  formed  from  such 
harmony  notes  and  attendant  embellishments  as  may  be  necessary 
for  its  construction.  At  the  third  measure,  form  a  new  subject,  to 
be  imitated  as  before  in  the  fourth  measure.  This  process  is  to  be 
continued  in  each  succeeding  two  measures  to  the  end. 

In  selecting  notes  for  the  imitation,  choose  such  as  will,  in  con- 
junction with  the  germ  notes,  best  represent  the  chord  of  which  they 
form  a  part,  care  being  exercised  toward  the  use  of  harmony  notes 
other  than  those  contained  in  the  germ  set.  These  are  preferably 
the  ones  forming  intervals  of  major  and  minor  3ds  or  6ths,  aug- 
mented 2ds  or  4ths,  and  diminished  5ths  or  yths.  Perfect  intervals 
and  minor  yths  are  also  admissible,  although  they  do  not  form  as 
satisfactory  combinations  in  two-voice  writing  as  do  the  others. 

Attendant  embellishments  should  be  added  in  such  maimer  as  to 
result  in  the  least  possible  harmonic  friction,  one  with  another; 
rhythmic  discrimination  should  be  observed  toward  the  employment 
of  successive  shorter  notes  in  one  voice  simultaneously  with  longer 
ones  in  the  other,  thus  giving  to  each  an  independence  and  indi- 
viduality especially  desirable  in  contrapuntal  composition. 


i88 


CUMULATIVE    HARMONY 


Limited  successions  of  3ds  or  6ths  may  be  admitted  to  good  ad- 
vantage, although  if  continued  beyond  the  number  of  three  or  four, 
the  voices  lose  more  or  less  of  their  character  of  rhythmic  independence. 


348 


I 


Subj. 


F=J^FF 


S^ 


^kf'     ^t^ 


(1^ 


Im. 


'=^=ii^ 


^^ 


*=^ 


rif  #  ff- 


s*-^ 


^^ 


t  ■      -f"   _  ■  ^i 


-i-^^ 


e=Si 


# 


E 


=^=ft^ 


(O 


I 


At  (a)  the  subject  formed  from  germ  notes  and  embellishments  is 
announced,  to  be  imitated  in  the  second  voice  at  the  second  measure. 


IMITATION 


189 


At  (b)  the  time  of  the  second  germ  note  is  anticipated  during  the 
latter  part  of  the  first  quarter,  in  order  that  the  way  may  be  cleared 
for  the  approach  of  the  notes  of  imitation  at  that  point. 

In  the  last  two  measures  (c)  the  imitation  is  not  expected  to  be 
complete,  a  portion  of  the  subject  only  being  imitated,  in  order  to 
effect  a  satisfactory  ending,  as  at  (c)  (d)  in  the  following: 


349 
y  —r-- ^  r ^ \ — i— — ->- 

—7S ■ 

v^=f — J  "-^^ 1  r  ^  r 

< 

y\  ^.j  1 — 

m-j^^jH'  ^^^^'  -I     ^n 

^'^  1^-^— ^ — 

The  germ  set  given  above,  as  well  as  those  that  follow,  should  be 
worked  out  in  several  keys,  and  with  different  subjects. 

While  always  following  implicitly  the  directions  given,  the  student 
should  p)ersistently  seek  to  make  the  resultant  work  sound  musically 
satisfactory. 


350 

p 

-^— 

=^T* 

— •-=- 

-#• 

• 

^ 

• ' 

— *-: 
-1 

+ 

» 

,» 

=t^ 

9    • 

-4- 

- ' 

=4^ 

-T— 

H 

1 

E^ 

0— 

^  '\  0 


^ 


s 


s 


wzz»-J-      M. 


i 


^if  fli^ 


^ 


i 


-  # — i^- 


g 


351 


fa 


5t     4^ 


m 


fi 


*^— <5*- 


I^ 


-fe 


J;-_* 


I 


19© 


CUMULATIVE   HARMONY 


111.  No.  01 


/\tv 


Bach,  "  Two-part  Invention,"  No.  i 


111.  No.  82 


Horatio  Parker,  "  Overture,  Fairyland" 


111.  No.  93 


Bach,  "  Two-part  Invention,"  No.  15 


:|i7T — ^ ^^ 


31 


^ 


S 


w 


Lm      q  ;p^^^Sg^^J5j?^^^P 


?^ 


i-si-ij — L^ — ^^ 


:?s=^ 


^^ 


CHAPTER   XXVIII 
CADENCES 

The  cadence  (or  close)  is  a  harmonic  device  consisting  of  the  final 
and  penultimate  chords  of  a  composition  or  phrase,  which  serve  the 
purpose  of  effecting  a  more  or  less  complete  finality. 

Cadences  are  divided  into  three  general  classes:  the  complete,  the 
incomplete,  and  the  deceptive. 

The  complete  cadence  consists  of  a  final  Tonic  preceded  by  a  penul- 
timate Dominant  or  Subdominant  chord.  Of  these  the  authentic 
cadence  (Tonic  preceded  by  the  Dominant)  is  the  most  common,  as 
well  as  the  most  complete  and  eflfective. 

It  appears  to  advantage  at  the  end  of  a  composition  or  phrase, 
and  is  practically  a  necessity  in  effecting  modulation.  While  the 
identification  of  all  forms  of  cadence  may  be  readily  determined  by 
the  last  two  chords,  in  most  instances,  one  or  more  additional  chords 
are  included  immediately  preceding  the  penultimate  Dominant 
which  have  an  important  bearing  on  the  progress  toward  complete 
or  temporary  finality,  and  tend  to  confirm  the  real  tonality. 

Of  these  preparatory  harmonies,  classed  as  pre-Dominant  chords, 
the  one  in  most  common  use,  and  which  seems  to  be  most  effectual, 
is  the  pre-Dominant  \  chord,  or  second  inversion  of  the  T  triad,  with 
the  Dominant  in  the  bass.  This  chord  generally  appears,  as  does  the 
final  T  chord,  on  the  accented  part  of  the  measure,  in  double  or 
quadruple  time.  Next  in  importance  for  this  purpose  is  the  S  chord, 
which  is  used  in  all  its  various  forms  and  positions  as  pre-Dominant 
harmony. 

The  chords  of  the  DS  (Dominant  of  the  Subdominant),  followed 
by  the  Subdominant,  and  of  the  DD  (Dominant  of  the  Dominant), 
preceding  the  penultimate  Dominant,  seem  effectually  to  prepare  the 
ear  for  that  chord  as  the  real  dominating  factor  in  key  identification. 

Here  follow  a  few  examples  of  authentic  cadences  extended  by 
pre-Dominant  chords  in  various  plans;  these  chords  are  so  enlisted 
for  the  purpose  of  intensifying  the  harmonic  progress  toward  the 
penultimate  Dominant. 

191 


192 


CUMULATIVE    HARMONY 


352 


D 


|S_        D 


W3 


d= 


D 


I^ 


m    a    fj 


s?^ 


-g— — ^?; 


-i5;«^ 


^ 


3^ 


1 


DS 


i 


D 


IjS    DD  T       D       T  TD|S^[S^D 


:!: 


=H — iS- 


g^^/  ,^;<5' 


=3= 


-g-ti^ 


:^=|l 


-a  &>g -^ 


2|22 S-- 


-?!5f- 


4       6        7 
2 


6      6 
5       4 


b7); 


The  student  should  form  cadences  in  the  manner  indicated  above, 
employing  three,  four,  or  five  of  the  S,  DS,  D  [S,  and  DD  chords  in 
their  several  species,  including  those  of  the  D)  and  the  D)).  This 
should  be  done  in  various  patterns  and  in  many  keys. 


m.  No.  94 


Harvey  Worthington  Loomis,  Song,  "At  Midnight" 


CADENCES 


193 


-m-^ 


down. 
Sva 


J     .     ^ 


1     1 


^^ 


+— n— 54- 


-=1— =»- 


Here  is  shown  a  DD  with  interpolated  T|,  the  |S^ancl  [|S  chords,  and  a  S  de- 
ceptive cadence,  followed  by  the  D))  as  a  confirming  chord. 

The  pedal  notes  (described  in  a  subsequent  chapter)  A  in  the  third  and  fourth 
measures  anfl  D  in  the  fifth  measure  should  not  be  considered  as  members  of  the 
attending  chords. 


111.  No.  95 


Beethoven,  "  Sonata,"  op.  14,  No.  2 


Here  may  be  seen  the  DS  to  the  S  chord,  and  the  DD  to  the  D  with  interpo- 


lated T«  chord. 
4 

111.  No    96 


DD 


Carl  Busch,  Song,  "  Crossing  the  Bar" 
3 6 5 


s 


K=?=? 


i^ 


-^—^ 


M 


S- 


:it=^ 


:9     *^f 


'fej: 


f=i 


iS 


:*=«: 


m^=^ 


I       I 


r 


^ 


f^ 


W^^ 


r 


194 


CUMULATIVE   HARMONY 


The  plagal  cadence  is  essentially  a  final  T  chord  preceded  by  a 
S  chord.  This  cadence  in  its  simple  form  has  long  been  in  common 
use  in  church  music.  It  has,  however,  at  times  attained  prominent 
positions  and  become  an  important  factor  in  the  works  of  the  master 
composers. 


353 


J21 


■J^ 


lA 


Modern  composers  have  employed  it  extensively,  using  the  many 
different  forms  of  the  S  chord  to  good  advantage. 


m.  No.  97 


Arthur  Foote,  "A  Lullaby" 


mm 


-»-^- 


333 


-3f- 


PP 


-X^ 


Ji 


^Zf 


-»- 


^ 


ppp  rit. 


S: 


tea 


-*-^ 


it^ 


li^ 


W 


-<s>-.- 


^^f^ 


m.  No.  98 


U. 


mm^ 


Campbell-Tipton,  Song,  "  The  Crying  of  Water" 


:i 


-«>-=- 


-« — ^ 


( 


tf 


m 


li 


-s^ 


-* !^-^ 


^ 


i^=S- 


ife2: 


m 


mp  X^ 


p: 


CADENCES 


195 


A 


^ 


i 


ty 


p. 


>~r"g"g 


EF 


^ 


^ 


■« 


SEte 


-)!-« 


»= 


Many  of  the  earlier  composers,  as  well  as  some  of  the  modern  ones, 
have  made  effective  use  of  the  Tierce  de  Picardie,  or  final  major 
T  triad  in  compositions  of  the  minor  mode. 

354 


^ 


-X 


1 


-fe: 


i 


T^ 


in.  No.  99 


Bach,  "  Prelude  IV  in  C#  Minor" 


m.  No.  loo 


m 


Arthur  Whiting,  "  Blow,  Blow,  Thou  Winter  Wind  ' 
rail.  ^ 


^^ 


i 


^ 


m. 


fi: 


^ 


0-i> 


196 


CUMULATIVE    HARMONY 

111.  No.  101 

Bach,  "  Organ  Fantasie  in  G  Minor' 


The  incomplete  cadence  (half  cadence,  or  imperfect  cadence)  may 
be  viewed  as  an  authentic  cadence,  incomplete  because  of  the  omission 
of  the  final  T  chord.  Its  most  famiUar  form  is  a  reversal  of  the 
complete  cadence  from  Dominant  -  Tonic  to  Tonic  -  Dominant,  the 
T  chord  appearing  in  its  second  inversion  as  a  pre-Dominant  4  chord; 
any  directly  related  chord,  however,  may  precede  the  Dominant  in 
this  form  of  cadence. 


355 


:=l2i: 


-s^ 


-f2- 


See  last  measure  of  111.  No.  85,  and  111.  No.  121 

L.  No 


m.  No.  102 

Cantando 


^B: 


P^ 


m^^-- 


PB: 


t% 


Arthur  Bergh,  "The  Raven" 


I     I 


-^— ^- 


/ 


\^ 


-J-, 


This  illustration  supplies  an  example  of  the  incomplete  cadence,  Subdominant- 
Dominant,  establishing  a  point  of  partial  repose. 


111.  No.  103 


*«fe 


CADENCES 

Wacner,  "  Tannhaueser  " 


197 


mm 


-n — i — ■^- 


Psi: 


■^ 


^=i^ 


-'S=r-r- 


3 


3^ 


The  deceptive  cadence  (false^  cadence,  or  interrupted  cadence)  con- 
sists of  the  D  chord  followed  by  a  chord  other  than  the  T  triad,  gener- 
ally by  the  submediant  chord  of  a  major  key  or  of  its  tonic  minor, 
or  by  a  form  of  the  Subdominant  chord. 


356 


l^^— 

«;■ 

\ 

J ^ 

^ 

^ 

1 1 

a 

m  s — 
1 

J 

g 

7 

7 

it^-  — i — 

P-i— 

^ 

«; 

i 

J ^ 1 

— i?^ 

357 


i 


* 


£ 


(W< 


y 


111.  No.  104 

lis 


W.  J.  Baltzell,  "Thistle-Down" 
I))  D       S 


198 


CUMULATIVE    HARMONY 

111.  No.  105  N.  Clifford  Page 

"  A  Thing  of  Beauty ' 


m^fm 


^ 


^ 


^ 


'S^ 


^')) 


b5 


111.  No.  106  Edward  Elgar,  "  My  Love  dwelt  in  a  Northern  Land  " 


A  A 

An  interesting  example  of  the  D^  chord  of  C  to  the  T  chord  of  A. 
presents  a  form  of  plagal  cadence  in  a,  intensified  by  an  interpolated  D' 

A  .  .  A 

C,  and  ending  as  a  Tierce  de  Picardie  in  A. 


It  also 
chord  of 


111.  No.  107 


Field,  "  Nocturne,  E  Minor ' 


This  subject  is  extensively  considered  in  a  subsequent  chapter. 

These  chord  combinations  are  of  frequent  occurrence  at  points  other 
than  at  the  end  of  a  phrase  or  of  a  composition,  with  the  chords  in 
their  various  positions,  and  are  termed  passing  cadences. 

The  D^  is  rarely  used  in  the  penultimate  chord  at  the  end  of  a  com- 
position as  a  part  of  the  final  cadence;  in  other  parts  of  a  composi- 
tion, however,  where  only  temporary  finality  is  sought,  it  is  used 
quite  frequently. 


CHAPTER   XXIX 
EXTENDED    CADENCES 

An  extended  cadence  consists  of  an  authentic  cadence  (described 
in  the  previous  chapter)  preceded  by  a  succession  of  chords  directly 
related  to  the  key  of  destination,  that  serve  to  intensify  the  harmonic 
progress  toward  the  penultimate  Dominant. 

The  effect  of  the  employment  of  such  successions  of  chords  is  to 
create  an  increased  atmosphere  of  expectation  and  suspense,  sub- 
sequently to  be  gratified  by  the  arrival  at  a  definite  point  of  destina- 
tion formed  by  the  authentic  D  and  T  chords  of  finality  and  repose. 

Extended  cadences  may  be  employed  at  the  close  of  a  composition 
or  at  the  end  of  a  division;  in  the  latter  case  serving  in  the  pre- 
vailing key  of  the  work  or  aiding  to  effect  an  important  modulation. 

The  chords  admissible  for  the  formation  of  extended  cadences  are 
as  follows:  the  chords  of  the  T,  S,  D,  the  DS,  and  the  DD.  These 
are  acceptable  in  all  positions  excepting  the  primary  positions  of  the 
D  and  T  chords,  which  are  to  be  reserved  as  the  penultimate  and 
final  positions  in  the  authentic  cadence. 


358 


#N^ 


DS 


DD 


DS 


DD 


D 


J  I  J      J 


^ 


-r- 


r=f- 


m 


A 


(o 

^ 


J(/._^(.,J 


m 


n^ 


J^ 


^^ 


i»-f=^ 


)) 


11 


«^)) 


6 
b5 


7» 


In  the  above  example  the  problem  set  forth  is  to  proceed  by  as- 
cending chromatic  progressions  in  the  bass  from  the  Tonic  toward 
the  Dominant,  to  which  note  the  chord  of  the  4  is  given,  followed  by 
the  penultimate  D^  and  final  Tonic  chords. 

199 


200 


CUMULATIVE    HARMONY 


It  will  be  readily  perceived  that  there  is  no  point  of  distinct  repose 
until  the  final  T  chord,  preceded  by  the  D  chord,  is  reached.  The 
direct  point  of  destination  is  the  Dominant,  which  is,  of  course, 
followed  by  the  Tonic  as  the  true  goal. 

At  (a)  appears  the  third  inversion  of  the  D))  chord  as  a  DS.  This 
is  followed  at  (b)  by  the  supertonic  as  the  fundamental  of  the  |S 
chord.  At  (c)  is  the  third  inversion  of  the  D))  on  the  DD;  at  (d),  the 
first  inversion  of  the  DS;  at  {e),  the  S  chord;  at  (J),  the  fundamental 
position  of  the  D))  as  a  DD,  leading  to  the  pre-Dominant  |  of  the 
authentic  cadence. 


359 


D 

I 


DS 


D 

I 


r 


D 

-J- 


f- 


J. 


-f=^ 


^- 


4  4 

3  2 


)) 


Here  the  bass  progressions  are  downward  from  the  Tonic,  F,  in 
similar  manner. 

Form  extended  cadences  in  various  keys,  proceeding  from  the 
Tonic  to  the  Dominant,  both  ascending  and  descending,  as  directed. 

The  student  may  now  form  extended  cadences,  modulating  to  the 
following  keys  in  the  given  succession,  using  the  final  Tonic  in  each 
key  as  a  note  of  departure  from  which  the  basses  should  proceed 
chromatically  to  the  penultimate  Dominant  of  the  succeeding  key. 
The  bass  progressions  are  to  ascend  or  descend  (as  the  case  may  be) 
in  the  direction  of  the  greatest  distance  from  the  note  of  departure 
to  the  note  of  destination,  for  the  sake  of  practice  in  acquiring  harmonic 
technique.  The  chords  available  for  this  purpose  include  those  of  the 
\S,  [|S,  and  S  depressed  3d,  and  the  D))  in  the  D,  DS,  and  DD 
chords. 


A     A       A      A 


C-a-e-G-b -A-f  S-D-d-F-g-d-B  7-F-a-C 


EXTENDED   CADENCES 


20I 


360 


« 


A 

(a)D 


DS 


DS 


D 


DS 


DD 


^ 


te 


r 


r 


r 


'P       ¥ 


--^ 


^ 


M. 


#6 
4 
3 


i 


«.i) 


7 


^ 


-Srs*- 


(^) 


A 

(d)S 


:)) 


1p — ^ 

l|4 
ill 


**6 
4 
3 


DD 


r 


=«r 


^ 


etc 


:i^ 


l|4 
113 


#6 

4 


•  •  •  •  •  A 

Starting  with  the  initial  key  of  C,  the  first  modulation  is  to  a, 
whose  Dominant,  E,  is  the  point  of  destination.  As  its  greater  dis- 
tance is  downward,  the  progressions,  for  the  sake  of  practice,  are 
made  in  that  direction  and  continued  as  in  the  previous  examples, 
to  the  Dominant  (E),  upon  which  the  preparatory  4  chord  is  followed 
by  the  penultimate  Dominant  leading  to  the  final  Tonic.  It  must 
be  understood  that  the  harmonic  successions  from  (a)  to  (b)  inclu- 
sive act  as  intensifying  chords  in  the  key  of  a.     As  the  Dominant  in 

A 

the  next  key  of  modulation,  d,  is  reached  at  a  greater  distance  by 
ascending,  the  progression  should  be  made  in  that  direction,  and  so 
on  through  the  given  series  of  modulations. 

This  mode  of  procedure  is  not  to  be  considered  as  the  best  means 
of  reaching  a  new  key  by  modulation,  but  rather  as  a  means  of  gain- 
ing a  familiarity  with  the  various  harmonies  at  one's  disposal  for  such 
purpose  through  an  intensified  close,  the  student  ultimately  selecting, 
in  composition,  such  as  may  seem  most  desirable  for  the  purposes  in 


202  CUMULATIVE    HARMONY 

\'iew.  It  must  also  be  borne  in  mind  that  the  enlistment  of  these 
chords  serves  to  create  an  atmosphere  of  homogeneous  harmonic 
variety,  and  always  tends  toward  confirmation  of  the  ultimate  Tonic. 
The  harmonic  schemes  evolved  from  this  process  may  be  formed 
into  accompaniments,  over  which  melodies  may  be  constructed  as  in 
previous  exercises.  In  each  key  the  duration  of  chords  may  be  re- 
duced or  extended  as  may  be  necessary  in  order  to  make  the  entire 
length  ot  eight,  sixteen,  or  thirty-two  measures. 


CHAPTER   XXX 

EXTRANEOUS   MODULATION 

Extraneous  keys  are  either  indirectly  related  or  foreign. 

Modulation  has  been  practiced  thus  far  only  to  directly  related 
keys,  a  passing  reference,  only,  having  been  made  to  the  exceptions 
in  serial  modulations  by  Rule  IV  (in  both  genders)  and  by  Rule 
V  (from  minor  to  major),  in  which  cases  the  modulations  effected 
are  not  to  keys  that  are  directly  related. 


361 

A 

(«)C 


d: 


Bb     {d)a. 


A 

{c)C 


(//)a 


^^^ 


:^=tt^ 


^5: 


W^ 


U 


l>7 


te 


b7 


-s>- 
7 


:^ 


-7^ 


-z?- 


At  (a),  following  Rule  IV,  by  taking  the  Subdominant  for  a  new 

A 

Dominant  a  modulation  occurs  to    Bb,  which  being  represented  by 

A 

a  signature  of  two  flats  more  than  the  key  of  departure,  C,  is  not  a 
directly  related  key.  At  (6),  following  the  same  rule  but  proceed- 
ing from  minor  to  minor,  the  key  of  modulation,  g,  is  indirectly 
related.     At  (c),  proceeding  from  major  to  minor,  by  Rule  V,   the 

A  ^  A       ^ 

key  of  d,  having  one  flat  more  than  C,  is  directly  related.  At  {d),on 
the  other  hand,  proceeding  by  the  same  rule  but  from  minor  to 
major,  we  reach  the  key  of  Bb,  which  is  not  directly  related. 

A  modulation  may  be  immediate  or  deferred.  It  is  immediate 
when  it  is  accomplished  through  the  use  of  the  D  chord  of  the  key  of 
destination  only. 

A  modulation  is  deferred  when  two  or  more  D  chords  are  utilized 
in  order  to  reach  the  key  of  destination. 


203 


204 


CUMULATIVE   HARMONY 


It  may  be  seen  that  by  the  rules  governing  serial  modulations  the 
note  for  a  new  Dominant  is,  in  each  case,  selected  from  the  diatonic 
content  of  the  key  of  departure  (the  key  from  which  the  modulation 
is  to  occur).  By  following  this  plan  modulations  may  be  accom- 
phshed  to  keys  which,  by  reason  of  their  gender,  do  not  bear  as  inti- 
mate relationship  to  the  key  of  departure  as  is  borne  by  directly 
related  keys,  but  are  sufficiently  close  to  invite  immediate  modulation 
to  them  without  impairing  the  general  harmonic  homogeneity.  Such 
modulations  are  to  indirectly  related  keys. 

Indirectly  Related  Keys 

Included  in  this  class  are  the  following: 

(i)  Those  reached  by  the  rules  for  serial  modulation  proceeding 
from  major  to  major  and  minor  to  minor,  when  they  proceed,  instead, 
from  major  to  minor  and  minor  to  major,  as  illustrated  in  the  following 
example. 


362 


in.  No.  108 


Beethoven,  "  Sonata,"  op.  i  lo 


^Jf 


!:& 


-■9-        -0- 


£ 


tr- 


m 


% 


'\-^- 

-t:^- 

£ 


He) 


))5)) 


Modulation  from  f  to  C  instead  of  to  c. 

(2)  Those  reached  by  the  rules  proceeding  from  major  to  minor 
and  minor  to  major  when  they  proceed,  instead,  from  major  to  major 
and  minor  to  minor,  as  in  the  following  example. 


EXTRANEOUS    MODULATION 


205 


363 


C   (III)     A 


111.  No.  109 


Dvoi^AK,  "  Walzer,"  op.  54,  No.  i 


Modulation  from  A  to  FS  instead  of  from  A  to  f«. 

(3)  As  exceptions  in  the  above  two  classes,  those  reached  by 
Rule  IV  when  proceeding  from  major  to  major  and  minor  to  minor, 
and  by  Rule  V  when  proceeding  from  minor  to  major. 

^^^       A  A  A  A  A  A 

C  (IV)  Bb  a  (IV)  g  a  (V)  Bb 


«- 


--^- 


st 


"^ 


--^^ 


^^ 


--m 


?7 


b7 


-bis^ 


(4)    Those   that   proceed    from  major  to  minor  when  proceeding, 
instead,  from  a  major  key  as  though  from  its  Tonic  minor. 

365 

A  A  A  A  A  A 

C    (a)  Ab  C   (d)  Db  C   (c)  Eb 


2o6 


CUMULATIVE   HARMONY 


At  (a),  by  taking  the  mediant  of  c  instead  of  C  we  reach  the  key  of 

A  A  /    \  .  A  ^ 

Ab  instead  of  a;  at  {b),  by  taking  the  submediant  of  c  instead  of  C 

A  A 

we  reach  the  key  of  Db  instead  of  d;   and  at  (c)  the  sub  tonic  of  c 
leads  to  Eb  instead  of  to  e. 

m.  No.  no  Chopin 

"  Nocturne,"  op.  37,  No.  2 


A  A       _  A  A 

Proceeding  from  G  to  Bb  instead  of  from  G  to  b. 


lU.  No.  Ill 


rgT 


Ethelbert  Nevin,  "  In  the  Night " 


|i2^tc 


^ 


itiE: 


t= 


b7 


^b. 


^ 


m.  No.  112 


Carl  Deis,  "  Waiting  " 


^^^ 


^ 


k 


m=^ 


f^r~rt 


^-  ^ 


-^=^ 


\C\)  4.  ^K 


ipc 


-(S2- 


i£|^ 


5fe 


^-^ 


l2z^ 


y?^ 


A  A  A  A 

Proceeding  from  C  to  Al>  instead  of  from  C  to  a. 
For  additional  reference  see  111.  No.  102. 


EXTRANEOUS    MODULATIOxN  207 

A 

A  table  of  the  indirectly  related  keys  to  C  would  be  as  follows: 

(i)fg,  (2)  ADE,  (3)Bb,  (4)  AbDbEb; 
and  of  the  indirectly  related  keys  to  a,  as  follows: 

(i)DE,     (2)f^,     (3)Bbg. 

It  is  not  to  be  understood  that  modulations  are  to  be  efTected  solely 
from  the  T  chord  of  the  key  of  departure;  they  are  fully  as  satis- 
factory when  proceeding  from  the  S  chord  or  the  D  chord. 

366 


i 


-7^ 


M 


:si 


^ 


-^5*- 


1^ 


Foreign  keys  are  those  extraneous  keys  not  included  among  the 
indirectly  related  keys. 

Modulations  of  this  class  are  rarely  satisfactory,  except  when  ac- 
complished by  the  enlistment  of  two  or  more  Dominant  chords,  in- 
volving one  or  more  passing  modulations  before  the  key  of  destination 
is  reached. 


A 

Among  the  foreign  keys  to  the  key  of  C  are  the  following:  c#,  f?f, 

A  A        ^,       A 

Gb,  B,  b,  d#,  etc. 


208 


CUMULATIVE   HARMONY 


Modulation  may  be  satisfactorily  effected  through  the  medium  of 
the  D^  chord,  confirmed  by  the  T  chord  of  the  key  of  destination ;  or 
by  means  of  other  forms  of  the  family  of  D  harmonies,  such  as  the 
chords  of  the  9th,  augmented  6th,  and  of  the  S  group  such  as  the 
Neapolitan  6th,  etc. ;  or  it  may  be  accomplished  through  the  aid  of 
ambiguous  chords,  that  is,  those  belonging  to  both  keys;  or  by  the 
various  intensifying  chords  of  the  extended  cadence,  involving,  per- 
haps, passing  modulations,  all  of  which  may  serve  more  fully  to  con- 
firm the  harmonic  change,  and  thereby  tend  to  increase  the  beauty  of 
its  general  tonal  effect. 


m.  No.  113 


4— i . — 


Wagner,  "  Lohengrin  " 


t^-^— te: 


fc|=±^ 


^ 


^ 


i^ 


>^=l^ 


^^- 


^^ 


-f9- 


£ 


r 


ni.  No.  114 


Poco  andantino 


Franck,  "  L'Organiste  " 


^"9^ 


3 


g^ 


^r^ 
K^/ 


Sj*^    Sj"^ 


7T" 


J?  w 


^^3^jc 


teeEiS3E£& 


^ 


^^ 


^-^r-^^^V 


EXTRANEOUS    MODULATION 


209 


The  student  would  do  well  to  evolve  and  classify  all  available  modes 
of  modulation,  and  through  practice  become  expert  in  applying  them 
in  problems  such  as  the  following:   modulate,   and  indicate  by  what 

A  A  A  AA  ^A  AA  AA  A^ 

rules,  from  C  to  Al?,  d  to  f,  A  to  C,  g  to  C,  F  to  bb,  Ab  to  eb,  B  to 

A   A      A 

C,  A  to  F,  etc. 

Transition  consists  of  passing  into  a  new  key  without  the  process 
of  modulation  through  the  use  of  a  new  Dominant.  Transition  is 
generally  to  the  major  or  minor  mediant  or  submediant,  to  the 
Tonic  major  of  a  minor  key,  or  the  Tonic  minor  of  a  major  key. 


368 


A 

c 

f) 

A 

E 

A 

C 

A 

Eb 

t 

k 

t 

A 

Ab 

6 

A 

C 

/    v 

a^ 

Jr      e> 

^ 

\\^. 

^ 

5'^ 

h  2? 

0 

m—^ 

-fLa 

— <9 

y^ 

— » 

ff«> 

— 15> 

K^— 

—S> 

\tK-«'— 

?f 

— S> 

b5 

—i9 

—& 

—s> — 

-9*9 

[>5 

—&— 

b      etc. 

'  (m\' 

h-. 

PJ- 

a 

UO 

1  V.^      <C/ 

'^ 

<3 

<» 

u. 

<3 

-s> 

\ 

d^ 

1/^        1 

Occasional  employment  of  transitions  in  the  composition  of  chorals 
is  advised. 


m.  No.  115 


yl 


A  llegro 

I 


gE£ 


Schubert,  "  Sonata' 


^3F^ 


IF=y 


^E^. 


^fcg 


J 


:^it=& 


4^^ 


-r 


f^-=^=^ 


jr— t^ 


ip=^^ 


5?^^ 


¥ 


^ 


3= 


2IO 


CUMULATIVE    HARMONY 


111.  No.  116 


Charles  Wakefield  Cadman 
"  Sonata  in  A  Major  " 


* 


I 


s=^ 


I      t 


H*=^=^ 


1 1    y  L 


'^  ^    '^  r  '^  r 


CHAPTER   XXXI 


SECONDARY   CHORDS   ON   THE   TONIC 

In  the  chord  of  the  Tonic  the  6th  may  be  substituted  for  the  5th 
to  form  the  Tonic  substituted  6th  chord.     Symbol    Tj  . 

This  is  an  application  of  the  submediant  triad  for  Tonic  harmoni- 
zation, and  will  be  utilized  and  analyzed  as  a  tributary  member  of  the 
family  of  T  chords.  It  is  most  frequently  used  in  fundamental  and 
primary  positions,  although  it  is  occasionally  employed  in  its  second 
inversion  as  a  4!  chord. 


360 


■u 


-7^ 


w 


-«r 


-KJ- 


-s*- 


-(=^- 


:(^): 


-75^- 


-m-- 


u 


AJ 


J6J 


jj 


The  Tonic  substituted  6th  chord  has  a  more  positive  local  signifi- 
cance as  a  primary  chord  in  the  major  mode  than  in  the  minor,  and 
the  Tonic  quality  is  most  in  evidence  when  the  chord  is  in  its  primary 
position,  with  the  6th  in  the  soprano,  and  preceded  by  the  D  chord 
in  one  of  its  various  forms. 

When  the  D'  chord  is  followed  by  the  primary  position  of  the  T| 
chord,  the  D^  resolves  to  the  T®. 


370 


TJ 


T] 


-7:)r 


-g<- 


-&■ 


-fi^- 


u 


u 


if 


4 

s 


iJ 


212 


CUMULATIVE   HARMONY 


When  the  D^  chord  is  followed  by  the  primary  position  of  the  Tj, 
the  9th  is  retained  as  a  common  tone  and  becomes  the  T^. 


371 


D 

TJ 

D))     TJ 

D 

TJ 

/    /              II 

1            1 

1             i     1 

1 

/  y       J          !    1 

!             1     1 

! 

J 

^^g— 

<w 

-^ ^ 

</ 

'^ 

_a_  ^ 

»         2^ 

^5^ ''-^ 

1  w ^_ 

< 

^ 

^^—.ir- 

i 

— s* — 

1 

1 

-^— g 

— ^ -S«— 

1              1 

-^g-:^-      ■ 

'  i^'                    '     ' 

^                  1 

1     1 

-, 

\rt^    A 

, 

— 1       J 

1 

— — ^ 

-^f              ' 

f^       <^ 

\     ^ — ^ 

—G> ^^— 

— -5^ — 

"l^^— ^ 

— (& — ^^ 

— 1 ■ 

9 

6| 

7))     ^ 

1 

7 

1 

7))    11 

y)^' 

^))1 

The  Dominant  chord,  in  one  of  its  various  forms,  followed  by  the 
major  T  chord  in  primary  position,  as  above,  constitutes  a  novel  and 
very  satisfactory  authentic  cadence.  The  5th  is  rarely  omitted  in 
the  fundamental  position  of  the  D''  chord  when  so  resolved. 

The  resolutions  as  given  above  may  be  applied  in  the  minor  mode, 
but  only  with  immediate  further  progression  in  view. 

In  the  minor  mode  the  primary  position  of  this  chord,  owing  to 
the  closeness  of  the  6th  to  the  5th,  has  a  distinctly  dependent  quality, 
as  though  the  6th  were  an  embellishment  above  the  5th  (a). 


372 


(«) 


D    {b)    Tl 


-ri- 


=i=- 


r 


r 

-I 


-<2- 


3: 


5^ 


^ 


In  the  fundamental  position,  on  the  contrary,  it  has  a  bold  individual 
character,  although  suggestive  of  further  important  progression  (6). 

When  the  Dominant  chord  resolves  to  the  fundamental  position  of 
the  Tj  chord  it  constitutes  one  form  of  the  deceptive  (false  or  inter- 
rupted) cadence. 


SECONDARY    CHORDS    ON    THE   TONIC 


213 


In  this  form  of  resolution  the  D  fundamental  is  not  doubled,  as 
parallel  octaves  would  result,  the  D'  resolving  to  the  T*  or  T^  in  the 
major  mode  and  to  the  T^  in  the  minor,  the  restriction  in  the  lat- 
ter case  being  a  precaution  against  augmented  progression. 


373 

A 

C    D 


i 


s 


-^ 


TJ 


D 


a  D 


TJ 


"m 


=^ 


w 


^- 


^ 


22: 


-rs- 


u 


_5| 


II 


The  deceptive  cadence  of  the  Ionic  minor  mode  may  be  used  in 
major  keys.  To  prevent  the  unsatisfactory  progression  of  an  aug- 
mented second,  the  D^  should  resolve  to  the  T^. 


374 


i 


:^ 


s»- 


iS^ 


7  b5j 

A  A 

In  the  above  example  the  D^  chord  resolves  to  the  T^|  of  c  instead  of  to  C. 

The  student  should  give  considerable  attention  to  the  analysis  of 
chorals,  hymns,  and  other  forms  of  composition,  marking  the  various 
chords  with  symbolized  figuring. 

m.  No.  117 


--L 


-J- 


LwoFF,  1833,  "  Choral  " 


:J=i 


5*=^: 


3 


d: 


^ 


-Ci- 


►J-4 — ^- 


i^^ 


6 
b5 


i^^ 


214 


CUMULATIVE    HARMONY 


i 


^^ 


m 


-^r 


-^ 


-si <s^ 


^ 


=te= 


ir. 


:^=^ 


^ 


t:: 


«6 
4 
3 


U 


-^ $!- 


s 


#-^ 


■*-  -^-  -^- 


t^ 


-(Z- 


^a '^- 


|6    6 
4 


7       ^ 


lA 


Notice  the  double  3d  in  change  of  position. 


111.  No.  118 


N.  Clifford  Page,  "  A  Thing  of  Beauty" 


^:m-r~^-^ti 


s 


-^—wt — ^ 


'^ — w- 


if=t 


^ 


*--^- 


Si- 


^EEfeEE^ 


7  ^  7)) 


7)) 


In  c  with  a  deceptive  cadence,  followed  by  a  modulation  to  f  through  the 
diminished  7th  chord. 


111.  No.  119 


Oscar  Weil,  "  Just  You  and  I,"  op.  31,  No.  i 


=:^1=:^:^-^-^-j'=^ 


SECONDARY   CHORDS   ON    THE   TONIC 


215 


111.  No.  120      E.  R.  Kroeger,  Suite,  "  Lalla  Rookh" 
,  u        Lento 


t}6 

il6         1 

4                1 

4-              1 

L2                IJ 

L2               i 

T  and  !]S  chords  alternating  over  the  Tonic  acting  as  a  pedal,  and  an  auxiliary 
above,  depressed  to  prevent  the  progression  of  an  augmented  2d. 


111.  No.  121 


Alexander  Ewing,  "  Choral" 


:4zi|^ 


^=r=^ 


P^g3 


S3 


^ 


u 


CHAPTER   XXXII 


THE   TONIC   ADDED    SIXTH   CHORD   T]\ 

In  the  Tonic  chord  the  6th  may  be  added  to  the  triad  to  form  the 
Tonic  added  6th  chord.     Symbol  Tjj  . 

This  is  an  application  of  the  submediant  7th  chord  to  Tonic  har- 
monization, and  as  such  is  classed  as  a  tributary  member  of  the 
family  of  T  chords. 


375 


ATI 

a  -i 


'iTll 


Til 


3 


i^ 


-ish 


T 


-f^ 


IIJ 


ill 


It  may  occur  in  any  of  its  positions,  but,  as  in  the  case  of  the  TJ 
chord,  the  Tonic  quality  is  most  in  evidence  when  it  is  in  the  primary 
position  of  the  major  mode,  with  the  6th  in  the  soprano,  and  preceded 
by  the  D  chord; 

The  D^  generally  resolves  to  the  'Pj  in  four-part  writing.  When 
the  D  or  D^  is  in  the  bass,  the  D^  moves  downward  to  the  T°. 

Examples  of  the  cadence  using  various  positions  of  the  Dominant 
chord  follow. 

376 


d= 


r 


d: 


-i5i- 


ill 


216 


'I! 
ill 


a 


THE  TONIC    ADDED   SIXTH   CHORD   T|] 


217 


-T5>- 


-Tir 


-(56. 


r 


-s^- 


r 


-(5(- 


-<5Z- 


6|i 

ill 


0) 


))  ^  3))  % 


The  T|  chord  preceded  by  the  chord  of  the  D^  is  much  more  satis- 
factory in  primary  position  when  written  in  five  voices,  particularly 
when  the  D^  chord  is  in  fundamental  position. 


377 


-St 


ty 


-5»- 


etc 


-&- 


As  the  notes  contained  in  the  6j  and  |||  chords  are  the  same  as  those 
forming  certain  S  chords  in  other  keys,  a  positive  identification  may, 
at  times,  be  obtained  only  through  the  succeeding  chords,  which  may 
indicate  a  modulation  to  the  key  of  the  Dominant  or  of  its  relative 
minor,  in  which  case  the  chord  in  question  becomes  an  intensifying 
factor  in  approaching  the  cadence  to  the  new  tonality. 


378 


i 


I 


if 


r 


^ 


-(*- 


r 


r 


t 


))  ^ 


6  7 

4  ^5 


2l8 


CUMULATIVE   HARMONY 


Here  the  indicated  T[l  and  Tj  chords  act  in  reality  as  -^  and  S 

chords  in  the  keys  of  G  and  e. 

Further  discussion  of  these  chords  will  appear  in  another  chapter. 

From  a  harmonic  structure  indicated  by  the  following  bass  set, 
develop  melodies  for  solo  voice  with  accompaniment.  Transpose  to 
other  keys  for  similar  treatment. 


379 


fm 


M: 


m^ 


S: 


7)) 


II 


)) 


1} 


A} 


■s 


ill        1^7 


'I! 
iil 


^^ 


i 


4 
3 


C6 

5        ^ 


U        #4 


)) 


Also  as  a  piano  solo,  thus: 


THE   TONIC    ADDED   SIXTH    CHORD   T[| 
An  additional  bass  set  for  similar  treatment  follows. 


219 


381 


t:*f>'<^ 


ir& 


1 


-z^ 


-25^ 
4 
3 


tl7)) 


•11  ^ 


U 


^i^ 


3 


liZ 


«5 

X 


«)) 


^li 


^ 


^^=1: 


^i^^ 


))     _6J        I 


9 

7 

#5 


1?9 

#7 


Al 


II    7 


All 


Transpose  the  above  bass  sets  to  several  keys  for  new  treatment. 

The  enlistment  of  this  new  branch  of  the  family  of  T  chords 
suggests  an  additional  rule  for  harmonization  of  melodies. 

The  sixth  of  the  scale  may,  at  times,  be  harmonized  with  the  Tonic. 
This  is  applied  to  best  advantage  when  the  sixth  of  the  major  scale, 
preceded  by  the  fifth  or  sixth  with  D  harmony,  occurs  on  the  accented 
part  of  the  measure. 


382 


r=«t 


-tfi'- 


A 


m 


4- 


1 


r^F 


U 


611 
ill 


The  Tjj  chord  as  an  additional  factor  in  harmonic  material  admits 
the  third  application  of  the  rule  for  passing  modulations,  those  pre- 
viously noted  being  the  DS  and  the  DD. 

When  the  T  added  6th  chord,  whose  fundamental  is  the  submedi- 
ant,  is  followed  by  the  S  substituted  6th  chord,  the  fundamental  of 


2  20 


CUMULATIVE    HARMONY 


which  is  a  fourth  higher,  the  T|  chord  may  be  altered  to  form  a  D 
chord,  eflfecting  a  passing  modulation  as  the  Dominant  of  the  super- 
tonic,  symbol  D[S. 


383 


$ 


T        T|i       [S 


D!S 


-<s*- 


r  r 


f- 
111 


i^^ 


r 


At  (a)  appears  the  T[j  chord  followed  by  the  [S  chord,  inviting  a 
passing  modulation  as  at  (b). 

All  forms  of  the  D  chord  are  admitted  in  passing  modulations. 


384 


T 


D[S 

I 


DD      D 


^^ 


--^ 


te 


^^r* 


J- 


ip: 


-;5»- 


7))    II 


^    *^)) 


-fs^ 


The  pre-Dominant  |  chord  is  frequently  interpolated  between  the 
chord  of  the  DD  and  the  succeeding  D  chord. 


385 


lis 

0          1 

DD 

T 

D 

1 

T 

/  V 

J             1 

; 

/T      '^ 

o.           ,\ 

f^. 

fn\      ^ 

^ 

^"^i^-i 

J^ 

\~\)                   U-, 

^^                  ^y^ 

$J 

1 

' 

i  ^«V           M            "- 

<n 

V^'        ^ 

^^ 

J 

\  '^               "i 

\                      1 

fi* 

\            1           t 

1 ■ r& J 

II' 


b7))       6 
4 


886 


THE   TONIC   ADDED    SIXTH   CHORD   Tjj  221 

DS  D|S^  DD  DjS^ 


Wz 


^ 


^4 


-?^ 


--^ 


~9- 
11 


■^^ 


4 
2 

DD 


??4 
2 

DIS 


DD 


_6J  b7))         [5 


D 


i^^ 


-^1=-'-^ 


^^ 


^ 


61       [6_       7))     6         4     #6U       [5_       ^4         6        _5J         ^ 
4J  4         2      b-V/  2       tjS 


DD 


DS 


4 

b 

DD 


a)) 


^g^ 


■*-^«L|, 


^ 


z^-       #6\\     6      5    7)) 


15  5Jj 


))  H)) 


4         6 
2         4 


■•r  »' 


It  was  noted  in  a  previous  chapter  that  the  DS  may  be  succeeded  by  the  |S 
or    !]S  chord. 

Extended  cadences,  as  given  in  a  preceding  chapter,  should  now  be 
formed  to  include  the  T  | ,   Tjj ,  and  D  [S  chords. 


m.  No.  122 


i 


&fi 


Wm.  J.  McCoy,  "The  Only  Voice" 


=^ 


S^!iEEi 


4: 


-#■ 


-z>9 


f^r? 


=3F 


fe 


i ± 


P^ 


^ 


/    y    !      .g? 


*^ 


s=r 


i 


^ 


r 


-<9^- 


'■^ 


P 


4^ 


m 


^r=^ 


■&=?=*: 


^-^X- 


222 


111.  No.  123 


CUMULATIVE    HARMONY 

Barnby,  "  NightfaU  " 


T^ 


i — r 


o>  . 


f- 


^iT-^ 


-«5 ^ 


-^2- 


^^ 


f 


^^ 


^  P 


n 


6  5) 


Ll 


Harmonize   the   following  germ   set,  applying   the  new  harmonic 
material  as  given  above. 


387 

i 

_^ 

1 

V^iil     1^             1    ' 

^ 

• 

0 

1 

^ 

^                    1         '■ 

/\   'i'^'  ^ 

1 

^ 

1                                        1 

i                '                 1 

rn  ^ \ 

« 

1                    ' 

1 

'        *    i 

VOJ    4-    i 

1 

1 

1 

iJ 

' 

JA + 


?Pi 


*t 


1^ 


-# P- 


I 


CHAPTER   XXXIII 

COMPOSITION   OF   CHORALS 

The  student  will  now  select  several  chorals  from  a  standard  hymnal 
or  choral  book,  to  be  used  as  rhythmic  patterns  for  original  melodic 
and  harmonic  treatment. 

The  harmonic  structure  should  consist  of  chords  belonging  to  the 
tonality  that  may  be  selected  for  the  composition,  with  certain  specified 
modulations  in  the  form  of  authentic  cadences  at  the  end  of  each 
section. 

The  hymn  is  to  be  divided,  at  points  suggested  by  the  divisions  in 
the  original,  into  four  sections,  the  conclusion  of  each  of  which 
should  be  in  the  form  of  an  authentic  cadence  to  a  directly  related 
key,  preceded  by  a  few  preparatory  or  intensifying  chords  selected 
from  those  available  in  extended  cadences. 

As  examples  of  such  chord  extensions  the  following  plans  are 
submitted : 

T«,  lS«,  Tt,  D^  and  T;  S,  DD|,  T|,  D^  and  T;  DS^,  S«, 
^■DBlt)),  rt,  D^  and  T;   T,  DT^jJ,  T|,  HS^,  D^  and  T.    These 

chords  refer  to  sectional  keys  of  modulation. 

A  plan  of  modulations  for  a  choral  is  here  suggested: 

The  first  section  modulating  to  key  of  mediant,  the  second  section 
modulating  to  key  of  Dominant,  the  third  section  modulating  to  key 
of  Subdominant,  and  the  conclusion  in  the  initial  key. 

Two  other  plans  follow: 

Modulations  to  Dominant,  supertonic,  submediant,  and  the  initial 
key. 

Modulations  to  mediant,  Subdominant,  Dominant,  and  the  initial 
key. 

Other  plans  may  be  selected  and  modulations  indicated  by  the 
student. 

Modulations  sho\ild  be  to  directly  related  keys. 

For  model  see  111.  No.  117. 

223 


CHAPTER   XXXIV 
CHROMATIC   OR   ALTERED    CHORDS 

Chromatic  or  altered  chords  are  those  in  which  one  or  more  harmony 
notes  are  chromatically  elevated  or  depressed  from  the  diatonic  con- 
tent of  the  immediate  key  without  necessarily  causing  a  positive  or 
passing  modulation. 

This  chromatic  alteration  generally  affects  the  D^,  which,  by  reason 
of  its  having  an  optional  resolution,  readily  invites  an  elevation  or 
depression  to  determine  definitely  the  direction  of  its  course  and  to 
aid  in  intensifying  its  progression. 

Chronologically,  this  was  at  first  accomplished  progressively,  by  the 
aid  of  chromatic  passing  notes  (a)  (a),  but  subsequently  the  chro- 
matically altered  notes  were  engrafted  as  essential  members  of  the 
chords  {b),  and  the  chords  classified  accordingly. 


388 


An  augmented  6th  chord  consists  of  a  D^  or  D^  chord  with  the 
fundamental  5th  depressed.     Symbol  <hD. 

This  chord  was  originally  used  in  the  second  inversion  with  the  de- 
pressed 5th  as  the  bass,  and  as  the  depression  of  the  5th  serves  to 
extend  the  normal  interval  of  a  major  6th  with  the  subtonic  leading 
tone  to  that  of  an  augmented  6th,  it  became  known  as  the  aug- 
mented 6th  (sharp  6th)  chord.  The  four  principal  species  in  their 
several  positions  and  with  their  resolutions  are  given  below,  with 
symbolized  figuring  attached. 

224 


CHROMATIC    OR    ALTERED    CHORDS 


225 


380 

French  6th  Chord 
D  T 


fe 


D 


D 


DD 


D 


ii 


-?:>' 


fr-"        ^ 


^ 


a,r    I 


(«) 


-J- 


-J 


I 


:§^ 


^ 


r 


I3 


DD 


i 


<hb5 


D 


DS 


6 

4 

DS 


tl7 


D 


5S: 


IP 


r 


-5&- 


J 


(O 


J 


(/) 


# 


E 


?^ 


ZSZ 


?;6 
4 

<r3 


i 


D 


i:  '^ 


<Hb5 


D 


D 


D 


^ 


-ZSZZL 


w 


I 


(^) 


-i 


(>^)l 

^ 


r 


e 


-^2- 


:^ 


-z?- 


<|-i>5 


J-bs 


<|'b5 


<pb5 


I.  The  second  inversion  of  a  D^  chord,  with  the  bass  depressed, 
is  known  as  the  French  6th  chord.  Symbol  <J^D.  This  chord  may 
resolve  to  the  T  chord  direct  (a) ;  to  the  D  chord  with  interpolated  4 
chord  {h) ;  as  a  DD  direct  to  the  D^  chord  (c) ;  as  a  DD  to  the  D^ 
with  interpolated  4  chord  {d)\  as  a  DS  to  the  S  chord,  toward  the 
authentic  cadence  (e)  (/") ;  and  to  aid  in  intensifying  modulations  to 
other  tonalities. 

When  the  depressed  5th  appears  in  the  soprano,  it  has  the  quality 
of  the  elevated  4th,  inviting  a  progression  to  the  degree  above  it,  and 
is  not  to  be  considered  a  very  definite  presentation  of  the  chord  {g). 

The  depressed  5th  and  the  3d  should  not  progress  to  a  unison,  as  ^ 


2  26 


CUMULATIVE   HARMONY 


one  of  the  voices,  failing  to  give  the  impression  of  resolution,  practi- 
cally disappears  (A)  (i).  At  (J)  these  two  voices  are  a  6th  apart,  per- 
mitting both  voices  satisfactorily  to  resolve. 


ni.  No.  124 

(.0 


Robert  Schumann,  "The  Two  Grenadiers" 

(a)  *  (^)   * 


(^) 


(O 


(d) 


i 


^ 


-^ 


4 


i; 


^3rw 


f^  r- 


■^: 


«6 
4 
3 


P^-G>- 


r. 


»^ 


S 


^ 


te- 


-I — h 


-<g- 


i^ 


At  (a)  (a)  the  fundamental  is  D,  at  {Jo)  (b)  it  is  C;  the  two  chords  at  (c)  and 
(d)  (fundamental  B)  are  alike  in  every  respect,  excepting  that  at  (d)  the  D^,  F#, 
is  depressed  to  Ft|. 


m.  No.  125 

Allegro  marcato 


Grieg,  op.  i6,  "  Concerto  A  Minor  " 


CHROMATIC   OR    ALTERED   CHORDS 


227 


,«-- 


^^ 


^ 


l^= 


8va. 


^^ 


:|^ 


i*-  — r  -< — r  -r  ■ 


t 


E 


4:- 


^-^4 


S 


53^ 


IT 


^ 


I    i  I    I  J     J,.    !    !  !    I- 


>  Ped. 


^ 


<^3 


'uj^- 


-=1 »- 


111.  No.  126 


Edward  F.  Schneider,  "  Triumph  of  Bohemia" 


^ 


'¥. 


I  ^ 


w 


-R 


r 


&^ 


|»6 
^3 


390 

Italian  6th  Chord 
( a )  D  T       ( * ) DD 


^6 

la 


D 


r 


^^ 


^ 


J 


J 


-^- 


<h6) 


<h«6)       6 
4 


n.  The  second  inversion  (from  the  D  fundamental)  of  the  D) 
chord,  with  the  bass  (D^)  depressed  and  the  D^  doubled,  is  known 
as  the  Italian  6th  chord.  Symbol  <hD).  Its  resolution  is  to  the 
triad,  one  D^  resolving  to  the  T',  and  the  other  to  the  T^,  as  at  (a). 
It  is  also  used,  for  intensification,  as  a  DD  toward  the  authentic 
cadence  {h).  Like  all  augmented  6th  chords,  it  is  best  in  the  original 
position  (with  the  depressed  D^  in  the  bass);  it  may,  however,  be  used 
in  all  positions. 


228 


CUMULATIVE   HARMONY 


111.  No.  127         Mozart,  "  Gloria,"  12th  Mass 


f^=bg 


«= 


ge 


-b'^r 


-J- 


zi5^ 


-Z5^ 


« 


-^J- 


±± 


-Sh 


b5 

301 

German  6th  Chord 
(a)DD  (/^) 


<l'S6) 


M^ 


:(g^ 


75H 


^J: 


r 


m 


III.  The  second  inversion  (from  the  D  fundamental)  of  the 
minor  D))  chord,  with  the  bass  (D^)  depressed,  is  known  as  the  German 
6th  chord  (a).  Symbol  <I^D)).  Its  best  resolution  is  to  the  4  chord. 
It  appears  to  great  advantage  before  the  pre-Dominant  \  in  the  au- 
thentic cadence.  In  the  example  the  D))  chord,  fundamental  D 
(DD),  with  the  fundamental  5th,  A,  depressed,  progresses  to  the  pre- 
Dominant  4  chord  on  G  (fundamental  C).  For  simplicity  of  notation 
the  minor  D^  is  frequently  written  as  the  elevated  D^  (6). 

This  is  equally  good  in  major  and  minor  keys. 

111.  No.  128        Frank  van  der  Stuecken,  "  Weave  in,  my  Hardy  Life  " 


/i^pi 


i 


^p=*=^^ 


i: 


p^ 


!Ei 


^ 


f! 


'')) 


<J-5, 


)) 


6 
<-3 


At  {a),  the  C#  is  an  enharmonic  change  from  Db,  so  expressed  for  simplicity 
of  notation. 


CHROMATIC    OR    ALTERED    CHORDS 

111.  No.  129                           Mabel  W.  Daniels,  "  Beyond  " 
4 3 


229 


Here  is  shown  a  French  6th  chord  constructed  from  a  DD,  with  interpolated  T|, 
a  retardation,  a  suspension,  and  a  D*  chord  merging  into  a  D^  chord.  The  reso- 
lution of  the  retardation  appears  with  the  interpolated  T^  chord  which  tempo- 
rarily represents  the  D  chord  that  follows. 


lU.  No.  130 


Arthur  Farwell,  "  Build  thee  more  Stately  Mansions" 


*    g  *    i  i^ 


4    1  X 


M 


3t-:;it 


-25^ 


J2^ 


|V.  V  V    V... 


t>k-  ^  I    1f^ 


^ 


*=^ 


a))    :)) 


^b5, 


««)) 


IV.  In  addition  to  the  three  spedes  given  above,  the  second  in- 
version (from  the  D  fundamental)  of  the  major  D))  chord,  with  the 
actual  bass  (D^)  depressed,  is  frequently  used  by  modern  writers. 
This  also  appears  to  excellent  effect  in  five  voices  with  the  fundamental 
included.     The  resolution  is  similar  to  that  of  the  German  6th  species. 

302 
Modem  6th  Chord 


^ 


i 


^=^ 
^ 


f 


1^ 


-^ 


fg       fg- 


Tir   ID): 


is: 


6 
5 


:?z= 


US 


9>9 


«6 
5 

<r4 


i 


230 


CUMULATIVE   HARMONY 


For  the  purpose  of  identification  the  fourth  form  will  be  known 
as  the  modern  augmented  6th  chord. 

While  all  species  of  this  chord  are  best  in  the  original  position 
(second  inversion  from  D  fundamental),  they  appear  also  in  the 
fundamental  position  and  all  inversions,  to  greater  or  less  advantage. 

Resolutions  of  the  augmented  6th  chord  to  the  various  species  of 
the  Tj  chord  present  many  very  novel,  as  well  as  charming,  harmonic 
effects,  that  are  much  practiced  by  modern  composers. 

The  student  should  practice  in  framing  original  harmonic  plans 
from  which  bass  sets  may  be  arranged  for  development,  as  heretofore. 

The  following  table  presents  some  examples  of  such  combinations. 
The  student  would  do  well  to  experiment  with  these  chords,  as  he 
may  be  assured  that  a  mine  of  harmonic  resources  will  be  opened 
to  him. 


393 


D 


D 


-si- 


D 


J 


r 


i>A 


J- 


t>^ 


T 
J. 


-fU- 


r 


i 


U 


6 
5 


U 


<r 


% 


U 


-s»- 


\>A. 


g; 


r 


f- 


4- 


irrJ: 


J 


r 

e 

■4 


6 
5 


u 


U  ^  i-^  %  '-'  k!  ^'))  % 


Work  out  extended  cadences,  effecting  modulations  to  the  follow- 
ing succession  of  keys  as  before  prescribed,  utilizing  the  T]  and  <1"D 
chords  in  their  various  forms  where  practicable. 


AAA.       A     AAA         A         AAAAA.A.A 

C-d-F-a-A-b-D-f#-F^B-b-D-<l-B-g-G-e-C. 


CHROMATIC   OR   ALTERED   CHORDS 


231 


394 


i 


i 


^jj^ 


m 


-PL. 


-^2- 


im:. 


r 


^ 


its 


-))^-Ii        .^)) 


^6 
4 
3 


I 
-<S»- 


¥ 


6 
5 


i 


:^ 


M. 


J 


-(&- 


:^ 


%: 


J 


-<>- 


LA. 


i:)) 


Fill  out  the  remaining  three  voices  from  the  following  figured  bass 
set,  working  out  various  forms  of  motus  in  the  individual  and  alter- 
nate voices.     This  may  be  done  in  several  keys. 

395 


i 


s 


3. 


Ij    Ll 


)r\))\ 


82))      iJl        \        bj) 


:^ 


s 


-i»-7^ 


<^i)    y) : 


]^m 


b7 


i^)) 


S 


S 


-^ 


£: 


u 


*^))M 


s 


i — 70- 


6-7 

4    - 

V      J- 


^   *'jj)|J    ib)! 


t»lj 


*T 


t:^ 


I 


?^)) 


232 


CUMULATIVE    HARMONY 


The  following  bass  sets  are  to  be  used  in  the  development  of  ac- 
companied melodies,  both  for  solo  with  separate  accompaniment  and 
for  piano  solo.     Transpose  to  other  keys  for  varied  treatment. 


396 


1 


IB: 


-'^— ttz^ 


S^^^=^^ 


-fSL- 


-?5*- 


'»  11^        '     m    I       D)  "a)) 


»i\\        6        11? 


5 


-(2 f9 


-4^ 


-S> (S- 


6|  9  5j  7 


7))     J6J       Ij^  6 


i|5  9 


m^^ 


MTl 


7)) 


307 


m^^^- 


j'=-^=j 


li& 


^-      ^ 


)) 


!        II  ^^5 


)) 


si: 


fe5±^Ei3i 


_6j   'b?)) 


b7)) 


^))    U      li^e 


:)) 


^S 


i;t=4 


3 


^^7— ^-^ 


r.'  fir^i)  ^^  *|j)"^' [f 


iti=fi*: 


IWl    ' 


<rb 


Harmonize  the  following  germ  sets,  making  especial  effort  toward 
enlisting  the  various  classes  of  harmonies  that  have  been  thus  far 
offered. 


398 


EB: 


^=^-=^fM^H=g 


CHROMATIC    OR    ALTERED    CHORDS 


233 


^m 


-^L 


a- 


X=r. 


E^E^^^^ 


i 


/  ^  ^»    r    I     i — n^ — I — -r^ 


I 


390 


^^^^r^=£jr"rif^^r=£"^ 


-^5f- 


i 


V        » 


ttYt 


i^ 


iiE 


S 


a 


:i?P^ 


:*^:^^ 


^^ 


^vw^ 


^ 


CHAPTER   XXXV 

THE   NEAPOLITAN  SIXTH    CHORD 

This  is  a  chromatically  altered  [6  chord,  with  the  6th  in  the  minor 
mode,  and  the  6th  and  3d  in  the  major,  depressed.     Symbol    I S^. 

In  the  formation  of  the  authentic  cadence  the  most  common  and 
effective  formula  for  extension  is  the  use  of  the  pre-D  |  chord  im- 
mediately preceded  by  the  S  chord  in  one  of  its  many  forms,  the 
most  popular  being  the  [S  or  ||S  chord. 

The  particularly  forceful  progressions  occurring  between  the  [S 
and  the  Tonic  4  chords  are  those  from  the  S^  to  the  T^  and  the  S® 
to  the  T^. 

It  may  be  noticed  that  in  the  minor  mode  both  of  these  progres- 
sions proceed  by  whole  step,  giving  the  impression  of  a  lack  of  har- 
monic affinity  between  the  two  chords.  In  order  to  overcome  this, 
early  composers  frequently  employed  chromatic  passing  notes  be- 
tween the  S^  and  the  T^,  thereby  bringing  the  two  chords  into  more 
intimate  harmonic  connection. 

The  chromatic  passing  note  (the  depressed  6th)  ultimately  became 
an  integral  part  of  the  chord.  Following  the  usual  custom  of  en- 
listing chords  of  the  minor  mode  for  harmonic  application  to  the 
major,  this  chord,  composed  of  a  minor  3d  (S  depressed  3d)  and  minor 
6th,  is  frequently  used  as  a  form  of  the  [S  chord  in  the  major  keys. 

It  is  most  commonly  followed  by  the  pre-D  I  chord,  often  by  the 
D  chord,  and  at  times  by  the  chord  of  the  DD  in  a  passing  modulation. 


400 


{a) 


(^,) 


S 


^- 


-zi- 


f- 


-ff?- 


-(^ 


-«$- 


J 


J 


\1 


b6 


-fZ- 

7 


234 


f- 


^ 


THE   NEAPOLITAN    SIXTH   CHORD 


-gr 


1 


235 


^ 


-og' 


-^ 


B^ 


•5*5>- 


-;S)<g- 


-Z5»- 


I'G  6 

b        4 


b6 


b6 


At  (a)  the  chromatic  passing  note  is  between  the  diatonic  S*  and 
the  T^;  at  (h)  and  (c)  the  B?  is  an  integral  part  of  the  Neapolitan  6th 
chord,  which  is  followed  by  the  pre-D  \  chord;  at  {d)  and  {e)  it  takes  the 
place  of  a  pre-D  chord  followed  by  the  D  chord ;  at  (/")  and  {g)  it  is  fol- 
lowed by  the  chord  of  the  DD,  the  two  serving  as  intensifying  pre-D 
chords;  at  {h)  the  Neapolitan  6th  chord  on  the  S  of  the  relative  minor 
is  enlisted  to  form  a  species  of  plagal  cadence.  Work  out  extended 
cadences  using  this  chord. 

While  in  modern  music  it  is  employed  in  all  positions,  care  should 
always  be  exercised  toward  preventing  disallowed  progressions. 


m.  No.  131 


W 


Chopin,  "Waltz,"  op.  34,  No.  2 


5^ 


^—t 


\f-%-    #- 


i 


^t-t^ 


4^^ 


Ib6 


While  this  chord  progresses  more  frequently  to  the  T^  chord,  the  progression 
to  the  D^  chord,  as  seen  above,  is  not  uncommon  and  is  very  effective. 


236 


111.  No.  132 


CUMULATIVE    HARMONY 

LoEWE,  "  Ballad  of  Edward  " 


S5 


WTf 


m 


ft 


^  -^ 


1^ 


-9 — ^ 


:^^-^ 


^ 


^    -^ 


-# « — =- 


^ 


J^^ 


4 

b2 


111.  No.  133 


Eugene  Blanchard,  "The  Sea  Gipsy,"  op.  5,  No.  2 


^^^ 


:?^ 


-7g»rsr 


fr-^ 


?^^? 


a^-o- 


e 


-i&- 


S'^^ 


:li= 


-(2- 


£ 


S^ 


b  .  '^    z' 


J^6 


b6 


*  An  example  of  the  Neapolitan  6th  chord  on  the  \S  of  the  relative  minor, 
borrowed  for  use  in  the  major  mode. 

Fill  out  the  following  figured  bass  sets  in  four  voices  with  varied 
motus,  after  which  the  same  harmonic  structure  should  be  formed 
into  accompaniments,  with  melodies  constructed  thereon  in  different 
forms,  as  heretofore. 

401 


mi 


s 


^^= 


'I))      i-^; 


6  6 

5  4 


^i    9)  ^  4^' 


m 


^ 


^g 


U  7)) 


'I! 


6 


<Hb5 


b7 


m 


1)6 

4 

<^3 


9 

b7 


U 


<r 


)) 


s 


b6 


I 


THE   NEAPOLITAN    SIXTH    CHORD 


237 


The  student  may  also  write  a  melody  from  the  following  germ  set, 
which  is  to  be  harmonized  in  four  voice  parts,  using  various  species 
of  motus;  also  prepare  as  solo  with  accompaniment,  and  for  piano 
alone,  applying  the  new  harmonies  given  above. 


402 


P^ 


S 


i 


** 


:))  ^  V))     jn 


3 


^ 


^ 


S 


m 


^ 


i|7)) 


Al 


«y)   ''  U 


4 


^^ 


^ 


I 


? 


#4 
2 


<r 


Us 


s))  IJ] 


lb6 
It 


^ 


CHAPTER   XXXVI 


AUGMENTED   FIFTH  CHORDS 

An  augmented  5th  chord  consists  primarily  of  a  major  or  minor 
triad  with  the  5th  elevated.  Symbol  J^.  It  is  the  outcome  of  the 
practice  among  early  composers  of  intensifjang  the  progression  of 
voice  parts  that  move  a  whole  step  from  one  chord  to  another,  by 
means  of  chromatic  passing  notes. 

They  occur  in  the  T,  S,  and  D  chords  of  major  keys  and  in  the  S 
chord  of  minor  keys.  As  the  diatonic  degree  above  the  T^  and  D^  in 
the  minor  mode  is  only  a  half  step,  the  opportunity  for  chromatic 
intensification  by  elevation  is  not  available  in  those  chords. 


403 


{a} 


ib) 


(O 


(^) 


(f) 


i 


E 


t3 


1^ 


?«3 


--P^ 


-^ 


^^i> 


%  step 


At  (a),  (c),  and  {e)  are  given  examples  of  intensification  of  pro- 
gression  by  chromatic  passing  notes  in  the  primary  chords  of  C,  and 
at  (g)  the  same  in  the  S  chord  of  a. 

At  (6),  (J),  (/),  and  iji)  the  chromatic  passing  notes  are  enlisted  as 
integral  parts  of  the  chords;  at  {i)  and  {])  the  T^  and  D^  in  a  pro- 
ceed upward  a  half  step,  forbidding  the  entrance  of  a  chromatic 
passing  note  and,  for  the  same  reason,  the  formation  of  an  aug- 
mented 5th  chord. 

A  table  of  augmented  triads  available  for  use  in  immediate  succes- 
sion is  given  in  a  subsequent  chapter. 

238 


m.  No.  134 

All"  ritmico 


AUGMENTED    FIFTH   CHORDS  239 

Arthur  Foote,    "  Flying  Cloud,"  op.  73,  No.  4 


^its 


The  harmonic  plan  of  the  above  is  as  follows: 

111.  No.  135 


The  S  augmented  5th  chord  (^S)  of  the  relative  minor  mode  is  used 
in  the  major,  and,  conversely,  that  of  the  relative  major  is  used 
in  the  minor;  the  progression  to  the  following  chord  in  both  cases 
being  governed  by  the  prevailing  gender. 


404 


At  (a)  the  ^S  of  a  is  used  in  the  key  of  C,  to  the  D  triad  of  which 

A 

the  chord  progresses.  At  (6)  the  S  augmented  5th  chord  of  C  is 
used  in  the  key  of  a,  the  progression  being  to  the  D^  chord  of  the 
latter  key. 

Augmented  5th  chords  may  appear  in  any  of  the  various  positions, 
those  with  the  major  3d  being  most  satisfactory  for  inversion.  The 
^S  chord  in  the  minor  mode  occurs  less  frequently  as  a  chord  of  6  or  | . 

In  the  chords  of  the  D^,  the  D^,  and  the  D)),  the  augmented  5th  is 
frequently  used  with  most  satisfactory  results,  particularly  in  the 
D^  chord.  In  the  resolution  of  this  chord  the  T'  is  usually  doubled, 
although  the  D^  frequently  resolves  upward  to  the  T^. 


240 


CUMULATIVE    HARMONY 


405 


^ — ^fe— 1 

/!? 

T~^ — 1 

s> 

'fe ' 

o 

7 

f% 

-!/ 

*r 

,Y^ 

ff 

\         '''* 

^  ^~, 

e> 

^, 

V- 

7 

<2/ 

S 

-^ 

^ 

L) 

^ 

-i9- 

-TO- 

^ 

fm\'          ^ 

|<?J. 

r^ 

«• 

^— ' 

rj 

^,. 

^ 

0f^ 

i 


^6 
I  5 


I     2 


f^)) 


-&- 


1^ 


-Pi^6 


^9      _6J  ^7 


111.  No.  136 

JA 


Oley  Speaks,  "The  Lassie  I  loved  Best 


m 


pS4=p 


^ 


i 


p^a 


|fc¥ 


— ^-H^ 


^IJ: 


r^^ 


'^. 


!ia 


3<=*: 


^ 


3i!=«t 


^^7 

liiS 


2. 


The  demands  in  resolution  of  the  ^D  chord  frequently  overshadow 
those  of  the  resolution  of  the  D^  to  the  T^,  as  may  be  seen  below, 
m.  No.  137  Wm.  R.  Chapman,  "  This  would  I  Do  " 

»        I 


^     t 


AUGMENTED    FIFTH    CHORDS 


241 


The  chord  and  symbol  at  (a)  will  be  described  in  a  subsequent 
chapter. 


in.  No.  138 


Wilson  G.  Smith,  "  Fulfillment " 


1^;^=^ 


^ 


ms 


'f  i'U^ 


^^ 


^« 


t§^ 


!•)) 


m.  No.  139 


George  W.  Chadwick 
"  A  Ballad  of  Trees  and  the  Master  " 


3: 


M^ 


t 


^ 


— ^ 

for  -  spent 


^ 


Clean 


-Oh 

In  -  to      the  woods 


i 


#=^ 


* 


-51- 


f 


5^ 


te==^ 


"»'•))  •))   ra 


The  harmonic  plan,  without  the  embellishments,  follows.  Note  the  D^  resolv- 
ing to  the  T^  in  the  bass,  as  may  be  found  in  the  works  of  Haendel  end  his 
contemporaries. 


in.  No.  140 


"^ 


;■&- 


^ b^- 


■•»  •))    ra 


--^ 


242 


CUMULATIVE    HARMONY 


Other  chords  of  the  7th  with  augmented  5th  will  be  referred  to  in 
another  chapter. 

Additional  rule  for  harmonization  of  melodies:  When  the  elevated 
5th  of  the  Tonic,  Subdominant,  or  Dominant  is  followed  by  the  next 
diatonic  degree  a  half  step  above,  it  may  be  harmonized  with  the 
augmented  5th  chord  (^5). 

The  following  bass  set  is  submitted  for  various  modes  of  treatment, 
without  and  with  embellishments: 


406 


^ 


-5*- 


-5^ 


^^ 


-r 


-r 


S 


-z^ 


J2^ 


r  r 


-^        a ^ — ii^— 


r 


-s<- 


r? 


^^ 


J>6    J>b7 

U  Us 


^#5 


3J 


^^6 
2 


f1))f^ 


S^ 


^b7 

Us 


f,;)) 


^ 


'^IIJ 


<r 


|b6 

lb 


6 
b5 


S 


He 

4 
3 


^E&d23t 


1    7         7 

|b5  i* 


^#6 
4 

b 


))'  \^m  ^i 


b    1^6 

^b5 


£ 


)) 


^       ^ 


I 


%^ 


^6 
5 


^7     b7 


b6|     ^7 
6 


7)) 


6      6 
5     4 


Here  also  is  given  a  germ  set  to  be  harmonized  in  various  forms 
without  and  with  embellishments. 


407 


ii± 


^^^^ 


n  {^-gf- 


i^£ 


:^-3f^- 


4: 


I 


=1^ 


-^a- 


rg  •  r? 


AUGMENTED    FIFTH    CHORDS 


243 


In  recent  compositions  the  D^  is  occasionally  elevated  and  de- 
pressed simultaneously,  the  elevation  resolving  to  the  T^  and  the 
depression  to  the  T^.  The  D^  here  frequently  resolves  to  the  T^. 
This  double  chromatic  alteration  of  the  D°  is  employed  in  the  D^,  D^, 
and  D))  chords  as  well  as  in  the  D  triad. 


408 


f^ 


[=A 


^ — ^ 


rr 


3t 


r 


*y 


r 


r 


tr-r 


5it 


^ 


m 


^=^ 


ft      fl)     fe)     fi) 


-p: 


<r 


)) 


p.yj 


-i 


-75>- 


-2?- 


d?^ 


f=f 


-^ 


A 


■r 


%^   -^ 


\>a_ 


-Z5^ 


-^- 


-fS^ 


-(=^ 


^ 


^ 


w  w  ^ 


9 

bS5 


%^)) 


^b  9 


409 


244 


CUMULATIVE    HARMONY 


It  may  be  noticed  that  this  form  of  the  D  chord  contains,  only, 
units  of  the  so-called  whole-step  scale  based  on  the  Dominant. 

Of  this  subject,  an  extensive  treatment  will  appear  in  a  subsequent 
volume. 

E.  F.  Schneider,  Music  Drama,  "Apollo" 
tr- 


Moderate 


i 


w 


BEE 


H^Sd^ls^i 


U 


M 


3p1z|^ 


^1 


P=F 


^ 


^e 


i 


^  ^  ^N s^ ^  ^    t:^ 

X5 

The  symbolized  figuring  here  given  is  with  disregard  of  the  pedal  notes. 

The  augmented  6th  chords  in  the  Tonic,  Dominant,  Subdominant, 
and  Dominant  of  the  Dominant  supply  the  units  for  a  scale  series 
in  whole-step  successions  beginning  on  the  Tonic,  Dominant,  Subdom- 
inant and  Dominant  of  the  Dominant,  upon  which  they  also  supply 
the  material  for  a  series  of  augmented  triads  and  their  inversions. 
These  chords  with  their  in>"ersions  may,  by  enharmonic  change, 
appear  as  a  series  of  augmented  triads  in  fundamental  position. 


410' 


=1^ 


-^ 


_£2_ 


^ 


DD 


^ 


^|: 


J- 


--^ 


■i^=^ 


^4- 


x>- 


-f^ 


1^-r 


^ 


*^ 


-p^ 


J 


hS^ 


^«'    f »      f !        1,5    f 


DD 


DD 


DD 


I 
D 


^6 
4 


f1 


:8^=ii=i^- 


-25^- 


r- 


=^ 


:«^^ 


fe=fc 


r(9- 


eES^t 


il 


D 


fl 


±=id=n 


f- 


J 


#=%- 


U,    -P#5     J>6      J>6      J>6      J>S6       !  I  '  '6      J>' 

-T"        I     »      U        l»        I*        I     4     -f#5    ^6      -f  J      f4        '■ 


«5 


CHAPTER   XXXVII 
IMITATION   OVER   GIVEN   FUNDAMENTALS 

The  student  may  now  undertake  the  writing  of  two  voice  parts 
contrapuntally,  over  a  given  fundamental  set,  with  specific  effort 
toward  imitation. 

The  subject  or  motive  may  be  chosen,  which  is  to  be  uttered  (fre- 
quently alone)  in  the  first  measure  either  by  the  first  or  second  voice 
and  imitated  in  the  succeeding  measure  by  the  other  voice.  During 
the  progress  of  the  imitation  the  voice  part  announcing  the  subject 
in  the  first  measure  should  continue  in  different  melodic  and  rhythmic 
succession,  as  heretofore  practiced. 

In  the  third  measure  the  same  subject,  accompanied  by  a  con- 
trasting melodic  succession,  may  again  occur,  K)  be  imitated,  as  be- 
fore, in  the  fourth  measure,  and  so  on  throughout,  always  with  due 
consideration  for  the  harmony  as  indicated  by  the  fundamental  set. 

Effort  should  be  continuously  enlisted  toward  the  evolving  of 
tuneful  melody  lines  in  both  the  subject  and  the  contrasting  voice 
part. 

The  parts  should  be  so  prepared  that  disagreeable  successions  of 
dissonant  intervals  may  be  avoided  and  that  the  general  effect  may 
be  musical. 


*"        Subj. 


Bass  set 


m 


^^^^^m 


^  f^i 


HS 


246 


CUMULATIVE    HARMONY 


>=^ 


S 


:|*i=ft 


^^- 


k  -r  f-  i-^-  f  -  ~^r-  rf"  f--^ 

H 1 1 bm^ ' 

!        I         '        '  '  '         '  "- 


Ei 


m 


:f^-^ 


t 


^ 


^   *■ 


^ 


/•^•^ 

Z7 

(t;.** 

— - 

f^ 

^ 

>-^"     /-^ 

^ 

--J 

(^> 

<CJ 

ej 

— « IJ 

The  subject  is  announced  by  the  upper  voice  in  the  first  measure, 
imitated  in  the  second,  reannounced  in  the  third,  and  imitated  again 
in  the  fourth,  to  agree  with  the  foregoing  directions. 

The  student  should  seek  to  individualize  the  various  voice  parts 
by  the  application  of  distinctly  different  rhythmic  and  melodic 
figures. 

Invent  new  subjects  for  similar  treatment  in  different  keys.  Two 
exercises  follow  for  further  practice. 

412 


l# 


M: 


fcfi 


~^^ 


-^-0- 


i^ 


j?=fc 


^ 

^ 


erfi: 


IS^ 


IMITATION    OVER   GIVEN    FUNDAMENTALS 


247 


^S^- 


*-   V 


T 


m^ 


j»^ 


etc. 


m 


I       ' 


^ 


m 


I 


-|^ 


-s^ 


413 


m^ 


^- 


IS 


-;5^ 


m^ 


i 


s 


•^5*- 


i^ 


-25^ 


Imitation  in  three  voices  is  developed  in  similar  manner,  with  the 
subject  appearing  in  a  selected  voice  part  at  the  initial  measure  and 
imitated  by  the  other  two  voices  in  succession.  The  subject  may  be 
announced  in  the  first  measure  and  imitated  by  the  other  two  voices 
in  the  two  succeeding  measures,  the  fourth  measure  being  occupied 
by  fragments  of  the  subject  or  by  other  contrasting  melodic  suc- 
cessions in  the  various  voice  parts. 

At  the  fifth  measure  the  subject  may  be  taken  up  as  before. 


414 


248 


CUMULATIVE   HARMONY 


^^=^ 


^ 


^  ^  J • *^ 


I  etc. 


/^.^ 


:f^:^ 


tT^^j^^^ 


iit 


H^- 


-^ — 

1 1 

4^ — f — 

— f^ — 

Cr- 

1— 

' si 

<s — 1 

g> 

(9 

1 

s) 

—9 

=1^ 


The  student  may  utilize  the  bass  sets  given  for  imitation  in  two 
voices,  for  similar  practice  in  three  and  four  voices. 


m.  No.  142 


Bach,  "  Prelude  VII,"  Preludes  and  Fugues,  Book  I 


5Ef 


p-m. ^  m  s     t-^- 

w. ^ ^ 


IW= 


^ 


e?3 


'm 


^,  *  * 


r^iat 


J: 


■^ 


-^-^ 


:5=^ 


--r 


^^^ 


:;773^=^ 


IMITATION   OVER  GIVEN    FUNDAMENTALS  249 

111.  No.  143  Bach,  •'  Symphony  in  C  Major  " 


3  #1  j#-^  J-^^#.  J- 


0..f>i^-- 


^ 


^s, 


n 


^ 


'— 1 — i — Um^ — ^ — ^Z^sC 


t= 


CHAPTER   XXXVIII 


ADDITIONAL  EMBELLISHMENTS 

An  arpeggio  is  a  melodic  deviation  from  a  note  of  the  germ  set  to 
another  harmony  note  of  the  same  chord. 

A  direct  arpeggio  returns  to  the  germ  note  from  which  it  deviates, 
before  the  succeeding  germ  note  is  reached. 

415 


i 


B: 


-Kt 


iBl 


^ 


Mi 


-m^ 


^— fS^ 


An  indirect  arpeggio  is  one  of  two  or  more  arpeggios  occurring  in 
succession  before  returning  to  the  germ  set;  it  may  return  to  a  germ 
note  other  than  the  one  from  which  it  deviated. 


416 


j- 


E 


-^c=^ 


-J. 


^i 


6 
5 

■J. 


■iS>- 


Other  embellishments  may  be  applied  to  arpeggio  notes. 

250 


ADDITIONAL   EMBELLISHMENTS 


251 


417 


i 


-^- 


W 


i 


U^-±A 


b: 


m 


le 


-7g- 


6 
5 

Form  various  figures  of  motus  in  the  soprano  from  the  germ  set  in 
the  following  exercise,  employing  combined  arpeggios  and  other  em- 
bellishments. 

The  same  may  be  done  in  the  alto  and  in  the  tenor,  care  being 
taken  to  prevent  unnecessary  overlapping  of  the  voice  parts. 


418 


|e: 


^ 


^^^S 


i^e 


^3 


J^,  rrTU-J-n-^J 


i**t 


f 


r 


m& 


r 

6 
4 


4  6       -f- 


I 


J    ^  J. 


etc 


^ 


^ 


^ 


r 


t 


? 


^ 


8^ 


-fsu 


mi 


i 


^-/s- 


■?5>- 


■^J &- 


^ 


I 


:^ 


:si 


Utilize  the  following  germ  set  as  a  basis  for  sprightly  melody  to  be 
constructed  with  the  aid  of  arpeggios  and  attendant  embellishments. 


252 


CUMULATIVE    HARMONY 


419 


■^m^ 


m 


r-*= 


te 


fe 


'»* 


fc* — f 


E^ 


3^S 


g^|E£ 


5J= 


^^ 


* 


If  ,r  ,^ 


-p #- 


£ 


Chromatic  passing  notes  may  be  used  between  harmony  notes  and 
diatonic  passing  notes  to  form  chromatic  scale  passages. 

420 


;es 


-Jb-iJ- 


^fc 


i 


az^ 


^-jjg^  ^g^ 


^*=i^ 


m 


6  7 


L7 


J 


£^^  r       f^=?r=^^ir 


^5t?fi2»r^ 


■HH 


111.  No.  144 


Chopin,  Etude,  op.  lo.  No.  2 


p=u^,u^^^-^m 


,Jm- 


^ 


ADDITIONAL   EMBELLISHMENTS 


253 


i 


1^  ^^  g^  g^z^^ij^m  j 


S 


4M- 


tM 


:«: 


(1: 


i«^ 


Harmonize  the  following  exercise  and  apply  chromatic  passing 
notes  to  form  a  sixteenth-note  motus,  first  in  the  bass,  then  in  the 
tenor,  alto,  and  soprano  in  turn,  and  finally  in  alternating  voices. 
Other  rhythmic  figures  may  be  employed  in  like  manner. 

The  customary  orthography  of  the  chromatic  scale  is  by  elevations 
of  diatonic  notes  in  ascending  passages,  and  by  depressions  in  de- 
scending. 

The  following  exceptions  to  the  above  may  be  noted :  in  ascending 
passages  the  depressed  seventh  of  the  scale  is  occasionally  used  in- 
stead of  the  elev^ated  sixth,  and  in  descending,  the  elevated  fourth 
should  be  used  instead  of  the  depressed  fifth.  (In  chromatic  no- 
tation, it  must  be  admitted,  composers  of  the  past  have  been  very 
uncertain.) 


421 


f 


L! 


Z~l 


^^  r  ^  *  r  t,fnriW==,  ,  i^   M  fa,  h^ 


i      L 


254 


CUMULATIVE   HARMONY 


^  if  ^  r^=ig==^^^.4g=f|^ 


-^-m- 


^Tt¥^=^ 


w=;^V\     ^  -^ 


i 


111.  No-  145 


Mozart,  "  Symphony  in  D  Major" 


^^^=^^,^^^^^^^^^_ 


111.  No.  146 


Beethoven,  "  Sonata  for  Violin  and  Piano,"  op.  96 


f^^pTr^ife^^E^^zpz^ 


^Mf 


r^-r^rW 


An  ornamental  anticipation  occurs  when  one  or  more  harmony 
notes  of  one  chord  are  interpolated  between  the  anticipation  and  the 
anticipated  note  of  the  succeeding  chord. 

Embellishments  or  combined  embellishments  and  harmony  notes 
may  be  employed  in  the  same  manner. 


422 


-i<--*-^-- 


^ 


iC^=^ 


1 


7^ 


4- 


f — r 
J i\ 


y  J  J 


1  -i 


TSH 


-(S- 


-^- 


~^- 


111.  No.  147 


•m 


^^ 


Adam,  "  Can ti que  de  Noel " 


i^rzf: 


^ 


^ 


r 


ADDITIONAL   EMBELLISHMENTS 


255 


Anticipations  of  passing  notes  are  occasionally  employed  with  ex- 
cellent efifect. 


423 


i 


j; .d. 


r 


^    J  -H — ^ — ^^^"""^ 


r 


J. 


-i'*'*^i>i>fj 


r 


^E^ 


-Kt 


4 


Suspensions  are  frequently  resolved  ornamentally  by  the  inter- 
polation of  other  notes  of  the  chord  or  of  embellishments  on  the 
suspended  note. 


424 

{a) 
5 9- 


^.1        H 


(*) 


i 


{c) 


^5?=^ 


^ 


is: 


<d) 


i 


^ 


<«) 


(/) 


^=*^:^ 


^#JiiP\- 


S= 


^ 


-75^- 


sr 


f 

5 


p4-ftr3   J  j    |:*=^ 

F-^J ^-J r 

*-! M    ^    rJ 

^ 

^:-^ 

— fi 

1 

1 

25* 

(S" 

e> 

jS" 

>:> 

2S6 


CUMULATIVE   HARMONY 


Example  424  shows  a  suspension  ornamentally  resolved  in  various 
forms,  such  as:  at  (a),  (b),  and  (c)  the  5th  of  the  chord  above  and 
below  interposed;  at  (d)  the  3d  of  the  chord  interposed;  at  (e)  the 
3d  and  5th  alternating  with  the  suspended  note;  at  (/)  changing 
notes  on  the  suspended  note;  at  (g)  combined  auxiliaries  and  har- 
mony notes;    and  at  (h)  combined  anticipation  and  auxihary. 


m.  No.  148 


Beethoven,  "  Sonata  in  C  Minor,"  op.  10 


Sa 


i 


4: 


-ISL. 


m^ 


^ 


^. 


Id2^ 


In  addition  to  the  suspensions  already  given,  others  may  be  added; 
in  fact,  modern  composers  admit  and  practice  the  suspension  or  re- 
tardation of  any  note  of  one  chord  that  progresses  a  diatonic  degree 
to  its  position  as  a  harmony  note  in  the  next. 


425 


3 — 9—8 


4 


^ 


^ji. 


5 6—5        9 -6—5 

I     -i--J-J 


-fa- 


^ 


(3) 


-^ 


-(2- 


m 


5^ 


-J^ 


J 


etc, 


J 


etc 


:J.^ 


=is 


^ 


fe- 


f^ 


8    1>7       r\8 


6 


6 
4 

bN 


7)) 


N5 


m.  No.  140 


li 


t^^ 
& 


l^4=¥- 


m 


i 


-J- 


A 


l\3 


Mozart 
3 7 8 


y—^^ 


-&<- 

^ 


N6 


S 


^ 


#1/8 


ADDITIONAL    EMBELLISHMENTS 


257 


Extended  passing  notes  are  frequently  inv'erted,  the  embellish- 
ment departing  by  degree  from  the  first  harmony  note,  instead  of 
approaching  the  second  one  by  degree.  The  departure  is  generally 
diatonic  above  and  chromatic  below.  They  are  classed  as  extended 
passmg  notes  inverted. 


426 


-^ — ^- 


J 


;*t 


■4 


:?z: 


J 


:4 


IlL  No.  150 


Beethoven,  "  Sonata,"  op.  109 


CHAPTER   XXXIX 


IRREGULAR   RESOLUTIONS   OF   THE   D^   CHORD 

Reference  to  the  transference  of  the  D^  from  one  voice  part  to  an- 
other has  aheady  appeared  in  this  work.  The  yth  is  also  subject  to 
ornamental  resolution,  effected  by  deferring  its  progress  to  the  T' 
through  the  interpolation  of  other  notes  of  the  chord,  of  embellish- 
ments, or  of  combinations  of  harmony  notes  and  embellishments. 

In  all  circumstances  the  7th  must  finally  resolve  to  the  T^  in  the 
same  voice  and  at  the  same  altitude  as  that  in  which  the  7th  appears. 


At  (a)  and  (b)  the  D^  above  and  below  is  interpolated;  at  (c)  the 
5th  is  interpolated;  at  (d)  the  5th  and  8va  alternate  with  the  7th; 
at  (e)  appear  the  changing  notes  E  and  G;  at  (/)  the  5th  and  8va,  and 
at  (g)  the  8va  above  and  below,  occur  in  conjunction  with  the  7th. 

In  the  chapter  on  cadences  the  deceptive  cadence  was  mentioned 
with  special  reference  to  the  D^  chord  followed  by  the  T)  chord  of  a 
major  or  minor  key  or  of  the  tonic  minor  of  a  major  key. 


IRREGULAR    RESOLUTIONS    OF    THE    D^   CHORD       259 


The  cfTective  device  of  deferring  the  resolution  of  the  D  to  the 
T  chord  by  interpolation  of  one  or  more  of  the  several  species  of  the 
Subdominant  family  is  considerably  practiced.  The  interpolated 
chord,  which  may  appear  in  any  of  its  various  positions,  should, 
when  thus  followed  by  the  T  chord,  be  considered  as  a  form  of 
plagal  cadence. 


428 


T=F 


[>6 
4 
2 


[1     l\    ' 


In  other  parts  of  a  composition  the  progression  of  the  D  funda- 
mental bass  is  to  the  S  chord  in  fundamental  or  inverted  position, 
which  may  be  succeeded  by  the  D  chord  in  one  of  its  various  positions. 


M^^..mu    .^H«-.^j»., 


^  :i4::i-Jill"^ 


26o 


CUMULATIVE    HARMONY 


When  the  resolution  of  a  D^  chord  is  to  be  followed  by  a  D'''  chord 
representing  a  different  tonality,  the  chord  of  resolution  is  frequently 
omitted,  the  D^  chords  following  each  other  in  immediate  succession. 
(See  DS  and  DD  chords.) 


At  (a)  the  D"  chord  on  D  is  resolved  to  the  corresponding  T  triad 
on  G,  which  in  turn  is  succeeded  by  the  D^  chord  on  G  duly  resolved 
to  the  T  triad  on  C.  At  (b)  the  resolution  of  the  D^  chord  on  D  is 
eliminated,  the  D^  chord  on  G  following  in  immediate  succession. 
At  (c)  and  (d)  the  same  process  is  carried  out,  the  successive  D'^ 
chords  on  G  and  D  appearing  in  the  same  manner. 

This  process  may  be  carried  out  in  sequence  through  a  considera- 
ble number  of  tonalities,  each  succeeding  D^  chord  representing  an 
implied  resolution,  as  well  as  a  positive  declaration  of  a  new  key. 


IRREGULAR    RESOLUTIONS   OF   THE    D^   CHORD       261 

The  passing  modulations  with  resolutions  at  (a)  and  (b)  are  re- 
peated with  the  resolutions  eliminated,  leaving  only  the  successive 
D^  chords  in  sequence. 


m.  No.  152 


Chopin,  "  Mazurka  in  G  Minor,"  op.  67,  No.  2 


Each  of  the  D^  chords  above  is  understood  simultaneously  to  resolve  to  its 
corresponding  T  choud  and  progress  to  a  D^  chord  for  a  succeeding  modulation. 
See  111.  153. 


m.  No.  153 


B 


?i=ii 


g± 


^ 


*5^ 


etc. 


Successive  D"  chords  frequently  appear  with  an  interpolated  ^  as 
a  pre-Dominant  chord  to  the  D^  chord  on  the  same  note  immediately 
following  it. 


432 


eJ  rj 


T 


f—r 


^i 


6 

b4 


^^- 


262 


111.  No.  154 


CUMULATIVE   HARMONY 

Beethoven,  "  Sonata,"  op.  13 


When  the  D^  progresses  melodically  one  degree  upward  to  the  T^ 
in  one  voice,  the  7th  may  be  doubled  in  another  voice  for  resokition 
to  the  T".  This  resolution  of  the  D^  to  the  T^  may  not  occur  in  the 
bass  part. 


433 


-fs- 


:si: 


l^-=.<fz 


In  the  minor  mode  when  the  bass  part  descends  by  degree  from 
the  Tonic  to  the  Dominant,  involving  successively  the  chords  of  the 
Tonic,  Dominant,  Subdominant,  and  Dominant,  the  normal  7th  of 
the  scale,  as  the  minor  3d  of  the  Dominant,  is  sometimes  used,  to 
avoid  the  descending  progression  of  an  augmented  second.  This  is 
known  as  the  Phrygian  cadence,  'and  is  found  occasionally  in  modern 
works,  as  well  as  in  those  of  the  older  masters. 

434 


S 


[6. 


IRREGULAR    RESOLUTIONS    OF   THE   D^   CHORD       263 


m.  No.  155 


Mendelssohn,  "Scotch  Symphony" 


(fen — j^ 


(« 


ii=^ 

£4=^ 


* 

i 


* 


i. 


-J-- 


m 


-ijg:     .- 


f^-- 


CHAPTER   XL 
SECONDARY    CHORDS   ON  THE  DOMINANT 

In  the  Dominant  chord  the  6th  may  be  substituted  for  the  5th 
to  form  the  Dominant  substituted  6th  chord.     Symbol  [D. 

This  is  an  application  of  the  triad  of  the  mediant  to  Dominant 
harmonization,  in  which  general  capacity  it  will  be  considered  in  this 
work,  both  for  harmonizing  melodies  and  for  analysis. 

As  in  the  cases  of  the  |S  and  the  T^|,  this  chord  has  the  greater 
local  significance  as  a  primary  chord  when  in  the  primary  position.  It 
may  be  used,  however,  in  all  its  various  positions  to  greater  or  less 
advantage. 

In  the  resolution  to  the  T  chord  the  D^  may  remain  as  a  tone  com- 
mon to  both  chords  and  becomes  the  T^,  or  it  may  ascend  to  the  T"" 
or  descend  to  the  T^.  The  D^  appears  to  best  advantage  in  the 
soprano. 

The  3d  of  the  scale  may  at  times  be  harmonized  with  the  Dominant. 

Discrimination  must  be  used  in  this  chord  similar  to  that  in  the 
D^  and  the  D))  chords.  If  the  D^  ascends  or  descends  one  degree 
before  the  resolution  of  the  chord,  it  is  not  an  essential  member  of 
the  chord  and  must  be  classed  as  an  embellishment. 


435 


W 


^ 


-f^ 


-tS- 


-7^- 


\ 


Examples  of  various  positions  of  the  chord  with  resolutions  to 
the  T  triad  are  here  given. 

264 


SECONDARY    CHORUS    ON    THE    DOMINANT 


265 


436 


^ 


i 


-r>- 


I    J 


r 


-75^ 


-^?- 


r-f- 


^^ 


[6- 


-s> s^ 


[6" 


[^ 


:^ 


[^ 


[fi- 


fe 


A         1             K 

pj=±l 

1=*=^ 

F^ 

v^=h. 

=^ 

-i h 

<        ,      1 

~r — ^— 

1         1 

—^ — «*— 

—^ »9— 

-\ — r 

1 

1           ! 

1          1 

^* 

f-^  ;g 

-f—T^ 

"^       J 

\IVl/                 ^ 

fp 

|0 

.-^                ^ 

^       (^ 

'                 1 

1*    1 

[6 

1^   i 

|6         6 

(T       6 

n 

1 

6 
4 

T  1 

6 
4 

-5*- 


-z^ 


-s>- 


-^ /S'— 


5-55*- 


gi     ^ 


f  r 

I      I 


fg     (^ 


-^- 


-<2- 


:^ 


[^ 


[5 


The  student  should  work  out  serial  modulations  by  several  rules, 
using  the  secondary  chords  on  the  Tonic  and  Dominant. 

Following  are  some  examples  of  various  resolutions  to  the  Tj  chord. 


437 

1 

1 

1 

/  V 

j 

1       1 

1           1        II 

•  <n            1 

1 

A           '     1 

1            ■         " 

■im 

^ 

-^    1 

'>          II 

v^)        J.          J. 

g         -.,        II 

1 

i 

1 

1 

r 

1 

1 
1 

1 

-(51- 

i 

1 

1 

1 
1 

\  'm\'        -S*              -'   "  1 

-,             -     1 

-^    ] 

'^           \ 

c 

£• 

'ly 

<5< 

■rj- 

rJ 

0 

— .9 _ 

\ — «-— 

[6 

1 

1 — ■9 — 

1 

[6" 

f2 

1 

1 ^— 

1 

1       '9 — 

1 

fe" 

(V       1 

1 

1" 

6 
4 

266 


CUMULATIVE    HARMONY 


m\ 


(5- 


-(»- 


AJ 


^ 


U 


F 


u 


[5- 


The  student  should,  at  this  point,  select  numerous  rhythmic  figures 
from  standard  hymns,  as  before,  for  application  of  the  additional 
harmonies  here  given  to  original  harmonic  and  melodic  combinations. 
Analysis  of  all  forms  of  composition  should  be  unremittingly  pursued. 

It  is  hoped  that  diligence  in  placing  these  examples  and  exercises 
and  hearing  them  played  has  not  been  relaxed.  The  value  of  the 
practice  of  mental  analysis  cannot  be  overestimated. 

With  the  inclusion  of  the  yth,  the  ID  chord  attains  an  additionally 
distinctive  Dominant  quality.  (Expressed,  Dominant  substituted 
6th  chord  with  7th  included.)     Symbol  ITP. 

In  the  ID^  chord  the  6th  resolves  preferably  to  the  T^  or  T^;  the 
presence  of  the  D^,  which  has  a  compulsory  resolution  to  the  T', 
causes  a  doubling  of  the  3d  when  the  D^  is  retained  in  the  same 
voice,  which  is  generally  not  as  satisfactory  in  four  voices  as  in  five 
or  more. 

The  D^  resolves  to  the  T^  or  descends  to  T^.  When  the  resolution 
is  to  the  Tj  chord,  the  D^  may  descend  to  the  T^|. 

A  few  examples  of  various  positions  of  this  chord  and  their  reso- 
lutions to  the  chords  of  the  T  and  Tj  are  here  given. 


438 


i 


^    II 


f- 


-—         ^ 


-dr 


-^ s^- 


SECONDARY    CHORDS    ON    THE   DOMINANT 


267 


i 


-zt- 


-Z5»- 


si- 


-(^ 


^6  r^ 


I 


The  sixth  is  rarely  good  below  the  seventh.     Such  arrangements  of 
the  chord  with  progressions  as  are  given  in  Exercise  439  are  uninvit- 
ing or  altogether  inadmissible. 
439 


W 


-T^- 


-i5?- 


T 


^Ei 


f- 


—7S 7->- 


I--  5  ^  15 

'  4  '  4 

|6  '  |g  1 

Add  the  three  upper  voices  to  the  following  given  bass  in  accord- 
ance with  the  figured  indications;  transpose  to  other  keys  and  work 
out  as  before.  The  student  should  then  take  the  harmonic  structure 
thus  formed  as  a  basis  for  an  accompaniment,  from  the  upper  three 
voices  of  which  a  melody  should  be  constructed  as  before. 

440 


%M 


1^ 


-(2d- 


m 


)) 


_5J 


4 
3 


t!7)) 


:=± 


m^ 


"i Ti- 


— z?- 


33 


xs*- 


D) 


!l' 


T=± 


^? 


7))      .6J 


t=^ 


-75*- 


#9 
7 


u 


61 


268 


CUMULATIVE    HARMONY 


Use  the  following  germ  sets  toward  the  constructing  of  melodies 
for  solo  with  accompaniment  and  for  piano  solo,  including  ID  chords 
in  the  harmonization  when  practicable. 

441 


^-li^^L 


'fSi-^ 


4=»=^ 


f 


iSSH^ 


iU     :^ 


1  J- 


etc 


-J — *- 


1   A 


t6  _5_| 

4 
3 


^2_._ 


■))      [6" 


-H2- 


442 

Germ  Set 


'«^ 


An^ 


Solo 


?«§ 


tH 


4=^ 


3t=*: 


:^^ 


Piano  Ace. 

3- 


*#=f 


^  -»--^--»- 


s 


::j: 


S6 

4 
3 

443 

Germ  Set 


^ 


S=£; 


Piano  Solo 


-^-^- 


sa 


43^ 


=£^=^1^ 


SECONDARY    CHORDS    ON    THE   DOMINANT  260 


444 
Germ  Set 


■g^ 


-«>-=- 


Melody  

4 


g^ggg^E 


:^^^^- 


Ace. 


«i 


lit: ^ 


[: 


^1    ^))  t 


6J       ILl 


445 


w 


w 


■w *-^ 


i^ 


m=^ 


:t=: 


=f===t 


ii^^ 


^1 


iii 


^*=ir 


^3^ 


i 


3J 


^  f-F-r 


J  2 


e 


?^i^ 


E^ 


fe^ 


T     '       1 


^^^i 


^ 


^ 


2  70 


CUMULATIVE    HARMONY 


-&-.         + 


-^^T- #- 


111.  No.  156 
» 
^^        ^  -g-     -^     -,^- 


:?4: 


Edgar  S.  Kelley,  Lady  picking  Mulberries 


-to * 1 — ^ 


-- — ^ 


Sii' 


1^. 


4: 


-=i— H 


-Ig    /^    !    ■ 


zu 


111.  No.  157 


ILZ  7 

McCoy,  "  Song  of  the  Flint"—  Cave  Man 


SlJ^F=i  y      ^ 


My 


wea - pon 


bor 


i 


p 


%-=^ 


::^= 


» 


tZJt 


^ =1-^- 


4=: 


7 
6 


111.  No.  158 


Wilson  G.  Smith,  "  Fulfillment " 


-cr 


^^ 


HH=2- 


^ 
W^ 


%-^-- 


-tr 


=^ 


7 
bb5 


r 

16 


-^ 


In  Illustrations  157  and  158  occurs  the  ID  chord  with  D^  included. 


CHAPTER   XLI 
DOMINANT   ADDED   SIXTH   CHORD 

To  the  D  triad  the  6th  may  be  added  to  form  the  Dominant  added 
6th  chord.     Symbol  iD. 

This  is  an  application  of  the  mediant  7th  chord  to  Dominant 
harmonization,  and  is  included  in  the  family  of  D  chords.  As  with 
other  secondary  chords,  its  primary  significance  is  most  pronounced 
in  its  primary  position,  with  the  6th  in  the  soprano. 

The  resolution  to  the  T  chord  is  much  the  same  as  that  of  the  ID 
chord.     The  D^  and  D^  resolve  as  in  the  D^  chord. 

The  D^  has  three  resolutions:  it  may  remain  as  a  common  tone  and 
become  the  T^;  it  may  ascend  to  the  T^;  or  it  may  descend  to  the  T^. 


446 


i 


-T^ 


-T^ 


T 


-^^ 


I 


16 
||5 


P 
||3 


r 


4: 


r 


^_i 


r 


-^2_ 


-O- 


:e=t 


I  I 


IT? 


P 


P 


The  resolution  in  various  forms  and  positions  of  the  flD  to  the  T] 
and  Tjj  are  here  amply  illustrated. 

271 


272 


CUMULATIVE   HARMONY 


447 


-75)- 


-J- 


i-i 


5 


-25»- 


f-T- 


r 


r 


rr 


J  -i 


J 


-z:*- 


H5^ 


^ 


r 


P 


iJ 


^ 


5II    ^?      5II   I?     -'     ¥ 


-75^ 


AJ 


-z?- 


-z?- 


-T5* 


-;5*- 


f 


r 


-^ 


-^      I 


-;5^ 


-Z5H 


r-f- 


r 


-i 


^-r- 
4  ^ 


114 


^ 


1} 


l|3 


6|| 


I   4 
13 


-tt:^ 


-s>- 


r 


r  r 


_;^ 


i- 


?— ^ 


T 


-(22- 


IT7 


P         _6j  P 


IJ 


U 


r 

IT7         ^         P 

The  fundamental  position  of  the  [D  and  [TD  chords  is  quite  effec- 
tive when  followed  by  the  fundamental  position  of  the  T^|  chord. 
In  the  resolution  of  the  IIU  chord  to  the  Tj  chord  the  D^  may  be 
omitted,  the  various  voices  proceeding  as  in  the  D'^  chord. 

448 


i 


-iri 'g- 


f^ 


:i= 


iJ 


r^ 


J- 


il 


T 


r 


-<a — 


etc. 


-<!y- 


P 


U 


P 


DOMINANT    ADDED    SIXTH    CHORD 


273 


Add  the  proper  voice  parts  to  the  following  bass  set  as  indicated 
by  the  symbolized  figuring  and  subsequently  use  the  harmonic  struc- 
ture for  accompanied  melody,  as  heretofore.  In  the  formation  of  the 
accompaniment  the  student  may  employ  occasional  embellishments, 
by  aid  of  which  most  interesting  accompanying  figures  may  be  evolved. 


449 


Melody 


rji- 


4 
3 


r 


6 
5 


-Z5»- 

^7 


* 


_5J      6' 

I 


i 


;)) ""  \ 


F=tS^|; 


P 


^  n 


4  ^ 


» 


liZ 


6 
4 

ill 


450 


^£=p: 


7))     ^ 


I^P^ 


Harmonize  the  following  bass  set  as  indicated,  and  work  out  with 
various  rhythmic  figures  as  motus,  in  each  voice  and  in  alternate 
voices. 


274 


CUMULATIVE   HARMONY 


451 


r* • — P* -m — i"it^^ w — z: 


-0- — ^ 


i 


^  i^  F  ^1  ^»^))^  '»    II 


'1  ^  *:))  * 


g 


^ 


-s»- 


"rl^^-^ 


p 


_5_|        9       J6j 
7 


jy^   t))''i^,l 


U    ')) 


g 


-(5!- 


'^^-- 


:K 


b7  b7))    b6j 


[L 


7-4 

b5-b 

b 


b7))      4\\    b6|       ||b7-4^         7)) 
s}}     a\      [j_b-b 


^- 


at=fe*=-J=:;^ 


))  ^ 


5- 


^^11 


II 


;s): 


111.  No.  159 


Wm.  J.  McCoy,  "  Egypt,"  Act  III 


111.  No.  160  William  Arms  Fisher 

"  The  Night  has  a  Thousand  Eyes  " 


'i^^ 


siJj^ 


"i^^ 


I  ^ 


9 


H 


1(9 


DOMLNANT    ADDED    SIXTH   CHORD 


275 


The  application  of  the  fiD  chord  followed  by  the  T|  chord  presents 
the  opportunity  for  the  third  in  the  series  of  passing  modulations. 

When  the  D  added  6th  chord,  whose  fundamental  is  the  mediant, 
is  followed  by  the  T  substituted  6th  chord,  the  fundamental  of  which 
is  a  fourth  higher,  the  ITD  chord  may  be  chromatically  altered  to 
form  a  D^  or  D"  chord,  effecting  a  passing  modulation  as  the  Domi- 
nant of  the  submediant  (  D  Tj). 


462 

Key  of  C 


1^^^ 

\ r 

^ 

.   I 

— <& — 

\ 

5* 

s' 

s>  

M 

a 

^ 

-.-..<J   

1 

19 1 

fS 

1 

5> 

-9- 

(52 

1 

« 

i3 

W 

r 

(Z 1 

1 

r 

7 

T^ ^ 

ri 

4 
3 

1 9 

6 

4 

s> 1 

7 

«/ 

A 

Key  of  a 


^. 


-y:t 


M- 


(o 


-C^ 


I 


ll«5 


At  (a)  occurs  the  fundamental  position  of  the  llD  chord  followed  by 
the  T|  chord  in  C,  with  the  fundamental  ascending  a  4th;  at  (6),  with 
the  same  fundamentals,  the  ITD  chord  is  altered  to  become  a  D^ 
chord  as  the  Dominant  of  the  submediant  [D  T|l,  effecting  a  passing 
modulation.  At  (c)  occurs  the  rfD  chord  followed  by  the  Tj  chord 
in  a:  at  id)  the  TD  chord  is  altered  to  become  a  D^  as  a  D  Tj,  form- 
ing a  passing  modulation. 


276 


CUMULATIVE   HARMONY 


453 


-s^ 


K=^^=^ 


-25*- 


-s»- 


r 


-25K- 


:«»= 


J- 


-i- 


l_        I 


-JS^" 


etc. 


=P=^i 


p  *t^  r^ML^ 


I      I 

6 


•r 


5      7))  Al 


:^ 


:^= 


-g^ »z^ 


^. 


^    I^J-Sllrf^- 


9 


7)) 


~-%^ 


-7ir 


^.^)) 


iU       ||4    «6U 

v/  [|3  bsy; 


t^ 


:^: 


-;5l- 


b7))         4 


Utilize   the  following  germ  set  for  composition  in  various  forms, 
applying  the  chords  recently  submitted. 
454 


±:fe 


:t^E 


l_^f 


£=5E 


>-^ 


-i-^ 


E: 


-(S- 


^P3^ 


:K 


±a 


&»r-p 


E^ 


=?^ 


-^-i-^ 


Extended  cadences  with  chromatic  bass  progressions  from  Tonic 
to  Dominant  in  selected  keys  and  from  final  Tonic  to  the  succeeding 
penultimate  Dominant  through  a  series  of  other  keys,  as  in  other 
successions,  may  now  be  worked  out,  to  involve  applications  of  the 

T|,  Til,  ID,  riD,  and  D  T^  chords. 


DOMINANT    ADDED    SIXTH    CHORD 


277 


There  are  to  be  found  in  the  works  of  recent  composers  (and  older 
composers  as  well)  occasional  examples  of  the  D^  substituted  for  the 
D^.  This  unit  (otherwise  known  as  the  Dominant  nth)  is,  with 
very  rare  exceptions,  an  embellishment  over  the  D^  or  under  the  D\  to 
one  of  which  it  progresses  during  the  life  of  the  D  chord. 

If,  therefore,  it  progresses  upward  or  downward  one  degree  before 
the  resolution  of  the  chord,  it  is  to  be  classed  as  an  embellishment 
and  not  an  actual  member  of  the  chord.  The  D"  here  often  resolves 
to  the  T^ 

It  occurs  also  in  conjunction  with  the  substituted  6th  to  form  the 
D  substituted  6th  and  4th  chord.     Symbol  |^. 

It  may  be  employed  with  the  D^  or  D^. 


lU.  No.  161 


Schumann,  Novelette,  No.  8 

•       •■         -A— 1 


(i5 


g3E 


1=^ 


'^U 


w^ 


^=^ 


ss 


^ 


-1=: 


t 


m.  No.  162 

Henry  Holden  Huss,  "Crossing  the  Bar  " 


CIL\PTER  XLII 


CHORDS   OF  THE   TONIC   SEVENTH   AND 
SUB  DOMINANT   SEVENTH 

By  adding  a  diatonic  7th  to  the  triad  of  the  Tonic  or  of  the  Sub- 
dominant,  the  chord  of  the  Tonic  seventh  [T"]  or  the  Subdominant 
seventh  [S~]  may  be  formed.  In  the  major  mode  these  chords  con- 
sist of  a  major  triad  and  major  7th.  In  the  minor  mode  the  T^ 
chord  consists  of  a  minor  triad  and  major  7th,  and  the  S"  of  a  minor 
triad  and  minor  7th. 


455 


i 


■p 


EJ(i)fc^ 


I 


The  fundamentals  of  all  chords  of  the  7th  are  naturally  inclined 
toward  other  fundamentals  located  a  perfect  fourth  higher.  As  may 
be  seen  in  Exercise  456.  the  fundamental  of  the  D''  chord  followed  by 
that  of  the  T  triad  (a),  of  the  sup)ertonic  7th  [  ^S]  followed  by  the 
D  triad  (6).  of  the  mediant  7th  [  D]  followed  by  the  submediant 
triad  [T^  ]  (c),  and  the  submediant  7th  [Tj]  followed  by  the  triad  of 
the  supertonic  [  [^]  (d)  are  examples  of  this  tendency. 


456 


ia)D 


T       {6)  ,[§       D       (<:)I'd        T        (^)TJ_|      [S^       {e)T      S 


-TSi- 


"W 


m\ 


ii 


This  is  equally  true  of  the  fundamental  of  the  T"  chord,  which  is 
best  succeeded  by  the  S  chord,  as  seen  at  {e)  in  the  example  above. 


TONIC   SEVENTH    AND   SUBDOMINANT   SEVENTH     279 

The  progression  of  the  fundamentals  in  each  case,  as  may  be  seen, 
describes  an  ascending  inter\-al  of  a  perieci  fourth,  which  is  recognized 
as  being  the  most  satisfacton,-  fundamental  progression  toward  tem- 
porar\-  or  permanent  repose. 

m.  Mo.  103  Edgar  S   Kelley,  op.  8.  No.  2,  *•  Israfel" 


m.  No.  164 


Clemevti,  "  Gradus  ad  Parnassum' 


m.  No.  166 


^n — agj 


im 


\riCTOR  Herbert,  "Natoma, 

S 


^=^ 


^5^ 


^E 


is: 


'^m—J-S 


ID 

8va. 


28o 


CUMULATIVE   HARMONY 


Schumann,  "Novelette,"  op.  21,  No.  2 


The  fundamental  of  the  S^  chord  is,  however,  denied  this  natural 
progression,  owing,  first,  to  the  fact  that  the  diatonic  fourth  above 
the  Subdominant  (which,  harmonically,  is  the  leading  tone)  is  not  a 
real  fundamental,  assuming  as  it  does  the  position  of  a  nominal 
fundamental  to  the  D)  chord. 

In  addition,  this  ascending  progression  is  that  of  an  augmented 
fourth,  which  is  not  considered  available;  the  descending  progression 
of  a  diminished  5th  is  but  little  better,  invohang  as  it  does  a  doub- 
ling of  the  leading  tone  and  an  absolute  failure  to  contribute  an 
impression  of  resolution. 


457 


S^ 


D) 


S7 


D) 


S^ 


D) 


i 


w 


-^- 


-^ 


d: 


5 


7  5)  7  5)  7  5) 

It  is  for  these  reasons  that  the  most  acceptable  progression  of  the 
fundamental  of  the  S"  chord  is  to  the  real  fundamental  of  the  triad  on 
the  leading  tone,  which  is  the  Dominant. 


458 


D 


w. 


tt 


m 


-^r 


>^ 


-(Z- 


TONIC    SEVENTH    AND    SUBDOMINANT   SEVENTH      281 


In  modern  music,  chord  progressions  from  the  S^  chord  to  the  D)) 
chord  are,  however,  occasionally  employed. 
459 

D))  S  D)) 


S 

I 


=S= 


V 


^ 


7)) 


These  chords  may  be  used  in  all  inversions,  no  member  being 
omitted  and  none  doubled;  in  the  fundamental  position,  however, 
the  5th  omitted  and  the  fundamental  doubled,  with  the  7th  in  the 
soprano  (Ex.  456),  is  quite  satisfactory. 

Harmonize  the  following  bass  sets  in  accordance  with  the  figuring, 
and  construct  melodies,  as  before. 

460 


-7Z^ 


-eZ- 


|5^ 


:)) 


)) 


5 


->sf- 


LLZ 


fP^ 


[f5 


??6\\  6   #5         ??6U  6} 


4 


#9 


I 


:|± 


6 


is: 


^ 


if? 


U 


-s*- 


11! 


461 


III 


)) 


7))      _6|        |]7 


b6 


2il 


u 


i 


282 


CUMULATIVE    HARMONY 


In  addition  to  the  chords  tabulated  above,  modern  compositions 
contain  many  effective  examples  of  the  chord  of  the  9th  on  the  Tonic, 
the  Subdominant  (see  111.  No.  165),  and  the  supertonic. 

This  subject,  as  well  as  the  more  extended  utilization  of  material 
drawn  from  the  overtonal  system,  such  as  the  so-called  whole-tone 
scale,  successions  of  augmented  fifths,  etc.,  will  be  treated  at  length  in 
a  subsequent  volume. 

The  exercises  offered  in  this  chapter  may,  as  heretofore,  be  utilized 
as  the  basis  for  accompaniments  upon  which  melodies  are  to  be  con- 
structed. Extended  cadences  may  also  be  worked  out  in  the  usual 
manner,  involving  the  recent  chords  contributed. 

A  table  of  the  direct  and  tributary  chords  included  in  the  three 
primary  families  —  Tonic,  Subdominant  and  Dominant — is  here 
given  in  C. 


462 
1 


(I): 


THE   TONIC    GROUP 


T  Triad 


(Also  occasionally 
with  depressed  3d 
in  major  keys) 


T^  chord 


^ 


r 


T  substituted  6th  chord 
[Submediant  triad] 


(Occasionally  with 
depressed  3d) 


T  augmented  5th  chord 


^S5 


T  added  6th  chord 
[Submediant  7th 
chordl 

(Occasionally  with 
depressed  3d) 


T^  chord 


TONIC    SEVENTH    AND    SUBDOMINANT    SEVENTH     283 


i 


i 


r.(&)< 


[6. 


THE   SUBDOMINANT   GROUP 

2 


S  triad 


(Also  with  depressed 
3d  in  major  keys) 


S  substituted  6th  chord 
[Supertonic  triad] 


(Also  with  depressed  3d 
in  major  keys) 


1^; 


S^  chord 


^(12) 


(2^ 


S  added  6th  chord 
[Supertonic  7th  chord] 


(Also   with  depressed 
3d  in  major  keys) 


im 


S  augmented  5th  chord 


-^#5 


(? 


:(|); 


{^ 


Neapolitan  6th  chord 

A 

in  a 


^6 


Neapolitan  6th  chord 


|b6 

b 


^ 


A)^=^- 


i 


(^=1 


S9  chord 


— W     (Also  with  depressed 
3d  in  major  keys) 


THE    DOMINANT   GROUP 

2 


r 


5i— JS*- 


r 


D  triad 


D^  chord 


284 


CUMULATIVE    HARMONY 

4 

Abbreviated  D"  chord 
[Leading-tone  triad] 


5) 


D9  chord 


m 


r/^)^ 


Abbreviated  D'  chord 
[Leading-tone  7th  chord] 


7)) 


^=^i 


^3 


French  6th  chord 


^ 


1=^ 


Italian  6th  chord 


Modern   augmented 
6th  chord 


D  substituted  6th 
chord 


}^'- 


;.»)) 


10 


German  6th  chord 


E21 


a 


^?t5 


12 


:|    D  augmented  5th 
chord 


D  added  6th  chord 


TONIC    SEVENTH    AND    SUBDOMINANT    SEVENTH      285 


13 


A 


P^ 


D  substituted  6th  chord 
with  7th  included 


^ 


14 


g      U     D   added    6th   chord 
with  7th  included 


P 

6 


(In  live  voices) 


15 


(i^ 


D  substituted  6th  chord  with 
7th  and  glh  included 

(In  five  voices) 


16 


-z^ 


D'  chord  complete 


(In  five  voices) 


17 


S^ 


a 


D  augmented  5th  chord 
with  7th  included 


u 


D  augmented  5th 
chord  with  7th 
and  Qth  included 


19 


i 


4 


-g^- 


I    ^ 


French  6th  chord  with 
D  added  6th 


20 

\^ — iSr 


4 

<-   3 


French  6th  chord  with 
elevated  D^ 


>86 


CUMULATIVE   HARMONY 


22 


Italian  6th  chord  with 
elevated  D^ 


7-b^ 


German  6th  chord  with 
elevated  D^ 


^#8 
6 


Modern  6th  chord 
with  fundamen- 
tal included 

(In  five  voices) 


D  substituted 
4th,  and  sub- 
stituted 6th 
and  4th  chords 


CHAPTER  XLIII 

SEQUENCES 

A  sequence  is  the  repeated  occurrence  of  a  melodic  or  rhythmic 
figure  upon  different  degrees  of  the  staff 

463 


i 


etc. 


E 


464 


(fe 


-i 


P=P= 


-<9~ 


etc, 


^ 


-(=2- 


r 


A  sequence  is  tonal  or  real. 

The  towa/  sequence  is  confined  to  the  diatonic  limits  of  the  key,  and 
is  subject  to  the  following  conditions: 

I.  It  is  the  general  name  of  the  intervals  (as  3d,  5th,  6th,  etc.), 
not  the  specific  name  (as  major,  minor,  etc.),  that  is  to  be  considered. 

II.  Augmented  intervals  may  freely  occur  in  any  part. 

III.  The  leading  tone  may  be  doubled. 

IV.  The  diminished  triad  may  be  used  in  any  position. 

The  above  privileges  (II,  III,  IV)  are  allowed  only  in  the  repetitions 
of  the  sequence,  not  in  the  original  figure.  The  final  repetition  also 
must  be  free  from  disallowed  progressions. 

V.  The  second  inversion  of  the  triad  is  usually  considered  un- 
available. 

VI.  The  original  figure  may  consist  of  two  or  more  chords,  with 
embellishments  if  desired,  and  may  be  repeated  upon  higher  or  lower 
degrees  of  the  staff. 

287 


CUMULATIVE   HARMONY 


465 

0  .->    n 

J 

1 

! 

1 

1 

J 

-i 

1 

! 

1 

.          .^ 

<=^ 

/T  •»               ^ 

^                 ^ 

rj 

r2 

\(\\  *i         >5) 

(2 

^ 

,^-> 

1-^ 

1         r-*       r 

Tq/Z      1^ 

--, 

f^           ra          r 

1*^               1 

1          PI           II 

-             1 

' 

1 

J^ 

1 

1 

1 

1 

1 

1 
i 

1 

1 
1 

_Jetc. 

/»)"-t                     '" 

1          r^ 

^1         r         1 

(fJ.fS 

1 

rj 

r^         \            1 

1^        1          1 

V-^*J      <•>          1 

' 

2J     1                     1 

1                        1 

' 

1 

' 

1 

The  tonal  sequence  may  consist  of  harmony  notes  only  or  it  may 
include  embellishments,  as  desired. 


466' 


-)f^ 


ii^ 


I        I 


-j- 


:^ 


The  rea/  sequence  is  of  a  different  character,  in  that  the  intervals 
employed  melodically  and  harmonically  in  the  repetitions  must  be 
identical  in  quality,  that  is,  they  must  be  of  the  same  specific  distance 
(as  major  2d,  perfect  4th,  diminished  7th,  etc.).  This  generally 
necessitates  a  passing  modulation  at  each  repetition. 


467 


*==!= 


m 


-(2- 


-.— sJ- 


Jt-^ 


^ 


#7 


#       «7 


T^6 

5 


#5        #7 


This  form  of  sequence  is  not  as  satisfactory  as  is  the  tonal  sequence; 
a  compromise  of  a  much  more  agreeable  character  is  frequently  formed 
of  modulations  alternating  to  major  and  minor  keys. 


SEQUENCES 


289 


468  A 

c 


A 


i 


J — ^- 


sf- 


-^- 


-U 


"S*- 


:S?- 


^^=^ 


f=^ 


-2^ 


i^rftM 


*s 


r 1- 


'■^ 


#^^ 


5        b7 


5       S7 


?5     it: 


m.  No.  167 


$m 


Bach,  "  Organ  Fugue  in  G 


^=^4: 


^ 


-*— t F- 


^^ 


^;«= 


I     I 


ii^J^ 


I 


SE 


W. 


111.  No.  168 


:i 


Bach,  "Organ  Prelude  in  E  Minor" 


tf 


J*     ^ 


-.^-^ 


m^ 


U     LU 


L7 


')) 


|5  r? 


,iK_ 


1^ 


1 — \ — \ — r 


T 


"isr- 


-.> — w- 


J^=^ 


J: 


r 


^ 


i 


^ 


I  '    IZ 

m    1^      , 


r 


290 


111.  No.  169 


CUMULATIVE    HARMONY 

Gounod,  "  Redemption  " 


Pedal  point,  organ  point,  pedal  note,  pedal  bass,  or  pedal,  is  the  use 
of  a  note  sustained  continuously  through  a  definite  portion  of  a  com- 
position while  a  succession  of  alternating  consonant  and  dissonant 
chords  are  being  sounded  in  the  other  three  voices. 

The  pedal  point,  in  most  cases  the  Tonic  or  Dominant,  is  placed 
generally  in  the  bass,  although  it  is  used  with  excellent  effect  in  any 
of  the  other  three  voices. 

When  occurring  in  a  voice  other  than  the  bass  it  is  termed  inverted 
pedal  point.  The  first  and  last  chords  should  be  in  accord  with  the 
pedal  note,  that  is,  they  should  be  chords  of  which  the  pedal  is  a 
note  of  harmony. 

The  harmonies  in  general  use  as  passing  chords  are  the  primary 
chords  of  the  prevailing  key  and  of  the  directly  related  keys.  In 
the  works  of  modern  composers,  however,  no  restrictions  seem  to  be 
considered  in  the  employment  of  harmonies  formed  by  combinations 
of  diatonic  and  chromatic  embellishments.  The  student  is  advised 
against  the  use  of  any  chords  excepting  those  drawn  from  directly 
related  keys  until  his  work  has  reached  a  mature  stage  in  its  progress. 

In  the  following  example  of  the  Dominant  pedal  point  the  chords 
are  all  of  the  prevailing  key.     The  embellishments  are  marked. 


460 


S3 


5? ^- 


-.i>-y       ^- 


^r^~W^ 


t^nH^^ 


An  example  of  pedal  point  on  the  Tonic  is  also  given. 


SEQUENCES 


291 


470 


In   the  following  examples  chords  from  directly  related  keys  are 
included. 

471 


■-te^   ^=^ 

=^-^ 

~* ^ M~\JM 

— fr- 

— ^ — # — 

^  1 

— ^^ 

J 

— ^ — 

^^^^=: 

-*      ^ 


^,  J— 1 —  ■      — f 


^^'^  *      rg- 


-=i=«td^ 


r 

^  ♦     -^-    -*^    — 


:^=4=i 


J2JL 


f  I       h  j^ 

— ^ — 

1        hi — 1 

—^ S"^-* — S"^-^ 

f>     ■ 

1      ^ 

J— 

p^^?E.E^= 

472 


DS         S 


A  J  ^  .ri^t^ 


T         DD 


2*=i= 


D  T       DD      D 


fe^'^_^=j;. 


^F^ 
J  ^ 


J.' 


i'  I 


H- 


^ 
^ 


292 


CUMULATIVE    HARMONY 


rX^ 


^=*: 


^ 


I       1 


.{?.^ 


^=^^=M: 


•— ^ 


T 


T" 


:^"??!i 


Double  pedal  point  is  frequently  used  to  excellent  effect,  particu- 
larly in  compositions  of  a  pastoral  character.  The  combined  Tonic 
and  Dominant  are  most  generally  used  for  this  purpose,  the  lower 
note  being  the  Tonic. 


473 


-^ ^ 


■±izMi 


nr-" 


:f^ 


-^H^rf^t. 


^-*- 


H^ 


-JE-±^ 


5^-  S^- 


-«-:— S- 


-6t-r 


Illustrations  of  various  species  of  pedal  point  are  appended. 


m.  N0.170 


W.  J.  McCov,  "The  Hamadryads" 


w= 


pp 


^m. 


t55: 


:5ia^*: 


:i=«t 


-^—m-^-x Sir 


%^,S^^jr= 


-£^-f 


SEQUENCES 


293 


111.  No.  171 

Andante  cantabile 


tq=dii-3i^=::^ 


^slE^l 


G.  W.  Chadwick,  "  Piano  Quintette  in  Ei>" 


-F-#- 


^      _*. 


-^-^5^ 


^ ^ 


:|tt=^: 


-^-^- 


:tK=^: 


I  ^ — '1       1     I 


111.  No.  172 


Cherubim,  "Quartette  in  C  Major" 


tf 


m. 


li 


l^=5-»^J^ 


-ft ^3f^^jr^:zmL^-»-^:M^  Hf^ 


;=!: 


yr 


-  #'^^^~  m  ^'  0-^-  0~  ^  0  ^- 


— I ai»*     r 


^^0:^0^0^Mf$M^ 


An  excellent  illustralion  of  Tonic  pedal  with  cnibellislunents. 


294 


CUMULATIVE    HARMONY 


111.  No.  173 


Wallace  A.  Sabin 

Prelude  to  "  St.  Patrick  of  Tara  " 


^ 


4: 


r  r 


^ 


0- — (• — ? 


i^fci: 


-(&-=- 


-••T-^V*- ^ ^ ^- »-- 


» 


:#: 


-=]: 


=t- 


-Gt-r- 


^2_ 


g-    ^    -Jl 


5^- 


=^: 


i.te 


i^: 


f 


?P=*: 


=|: 


=|r 


^ 


111.  No.  174 


PuRCELL,  "  Service  in  Bb  " 
J 


1===^ 


-;g< gJ       rJ 


-7^ ^       eJ       si- 


(S^ 


^^-&-^ 


-(2-     -s-- 


]ffi — ;$,- 


-fz — ;©- 


111.  No.  175 

:t2--3=zz: 


Heller,  "  Dans  les  Bois,"  op.  128 


'Az 


=1:»|: 


^r^ia 


I       I  I  


!ii^ 


I       I         !         J 


*t 


-4  -.*t 


^' 


H 1 1—' \-\— 

TX--    X 


liT 


r 


f 


-^ 


SEQUENCES 


295 


111.  No.  176 


E.  A.  MacDowell,  "Shadow  Dance" 


In  five-part  harmony  avoid  doubling  such  members  of  the  chords 
as  have  compulsory  resolution.  Those  best  suited  for  doubling  are: 
(i)  in  the  D^  chord,  the  D^  and  D^;  (2)  in  the  D))  chord,  the  D^  and 
D^.     Crossing  of  the  parts  should  generally  be  avoided. 


INDEX 


Abbreviated  Dominant  ninth  chord,  170 
Abbreviated  Dominant  seventh  chord,  So 
Abbreviated  minor  ninth  chord,  174 
Accompaniments.  34 

construction  of  melodies  over,  31 
Added    sixth    chord,    on    the    Dominant, 
2;  I 

on  the  Subdominant,  84 

on  the  Tonic,  216 
Altered  chords,  224 
Anticipation,  i  52 

of  passing  notes,  255 

ornamental,  254 
Appoggiatura,  14S 
Arpeggio,  definition  of,  250 

direct,  250 
Arpeggio  notes  with  embellishments,  250 
Augmented  fifth  chord.  238 
Augmented  sixth  chord,  224 

resolution  of.  225 
Augmented  triad.  17 
Authentic  cadence,  44,  191 
Auxiliaries,  definition  of,  136 

below  the   third  and  seventh  in  major 
keys,  138 

below    the    second    and  fifth    in    minor 
keys,  138 

below  the  seventh  in  minor  keys,  138 

extended,  141 

introductory,  148 

progressive,  150 

successive,  140 

Cadence,  definition  of,  191 

authentic.  44,  191 

complete,  191 

deceptive,  197 

extended.  199 

incomplete.  196 

passing,  198 

I'hrygian,  262 

plagal.  194 

Tierce  de  Picardie,  195 
Changing  notes,  152 
Chord,  definition  of,  16 

of  the  sixth,  25 

of  the  sixth  and  fourth,  26 

of  the  sixth  and  fourth.  Rules  I,  II,  III, 
IV,  78,  79 

of  the  sixth  and  fourth.  Rule  IV,  191 

of  the   sixth  and  fourth,  bass  doubled, 
24,  80 


of  the  sixth  and  fourth  between  Domi- 
nants, 91,  193 

of  the  Subdominant  seventh,  278 

of  the  Tonic  seventh,  278 
Chromatic  alteration,  definition  of,  6 
Chromatic  chords,  224 
Chromatic  passing  notes,  132 
Chromatic  progression,  6 
Chromatic  scale,  orthography  of,  253 
Chromatically    altered    notes,    how    indi- 
cated, 25 
Compass,  of  voices,  22 

for  accompaniment,  37 
Compound  passing  notes,  129 
Compulsory  resolution,  44 
Consonance,  definition  of,  13 
Contrary  motion,  definition  of,  20 

to  avoid  faulty  parallels,  41 
Counterpoint,  definition  of,  185 

Deceptive  cadence,  212 
Deferred  modulation,  203 
Diatonic,  definition  of.  2 
Diminished  intervals,  definition  of.  9 
Diminished  seventh  chord,  174 
Diminished  triad.  17 
Directly  related  keys.  63 
Discords,  definition  of.  43 
Dissonance,  definition  of,  14 
Dominant,  definition  of.  4 
Dominant,  of  the  Subdominant,  73 

of  the  submediant,  275 

of  the  supertonic,  220 
Dominant  added  sixth  chord,  271 
Dominant  ninth  chord,  162 

abbreviated.  Rules  I,  II,  III,  170,  171 

best  use  of  ninth,  165 

inversions  of,  164 

ninth  as  embellishment,  166 

ninth  ornamentally  resolved,  168 

not  used  as  penultimate  chord, 

resolution  of.  163 

with  augmented  fifth.  239 
Dominant  seventh  chord,  43 

abbreviated.  So 

as  intensifying  chord,  46 

deferred  resolution  of.  259 

determines  tonality,  43,  75 

exceptional  resolution  of  the  third,  68 

exceptional  resolution  of  the  fifth,  32.  46 

exceptional   resolution  of  the  seventh, 
49,  243,  277 


297 


298 


CUMULATIVE  HARMONY 


fifth  omitted,  45 

first  inversion  of,  48 

fundamental  position  of,  45 

irregular  resolutions  of,  258 

ornamental  resolution  of  the  seventh,  2  58 

resolution    of   the    third    in   successive 
Dominants,  74 

second  inversion  of,  48,  81 

successive  Dominants,  74,  90 

table  of  resolutions  of,  45 

third  inversion  of,  50 

third  and  seventh  not  doubled,  44 

third  omitted,  68 

with  augmented  fifth,  239 

with  depressed  fifth,  224 
Dominant  substituted  sixth  chord,  264 

with  seventh  included,  266 
Doubling,  definition  of,  19 

in  five-part  harmony,  295 

of  the  bass,  24 

of  the  leading  tone,  46 

of  a  note  dissonant  with  its  fundamental, 

44 
of  the  seventh,  46,  80,  295 
of  the  third,  19,  45,  83 

Embellishments,  definition  of,  103 

applied  to  arpeggio  notes,  250 

double  and  triple,  156 

list  of,  103 

on  accented  or  unaccented  part  of  bar, 
124 

symbol  of,  103 
Enharmonic  change,  definition  of,  54 
Exceptional   resolution,  of  the  Dominant 
seventh,  49,  227,  243,  276 

of  the  Dominant  third,  68,  213,  216 
Extended  cadences,  199 

with  chromatic  bass  progressions,  276 
Extended  passing  notes,  133 

inverted,  257 
Extraneous  keys,  203 
Extraneous  modulation,  203 

False  relation,  definition  of,  153 

when  not  objectionable,  153 
Faulty  doubling,  of  the  bass,  24 

of    a    note    dissonant    with    its    funda- 
mental, 44 

of  the  third,  19 
Faulty  parallels,  40,  105,  129 
Figured  bass,  25 
First  inversions,  24 

of  triads,  24 

of  Dominant  seventh  chords,  48 
Foreign  keys,  207 
French  sixth  chord,  225 

resolution  of,  225 
Fundamental,  definition  of,  16,  29 

most  suitable  for  doubling,  19 

nominal,  80,  170 


progressing  upward  a  fourth,  73 
real,  80,  170 
Fundamental  position  of  chords,  24 

Germ  set,  definition  of,  132 

for  melody  with  accompaniment,  158 
German  sixth  chord,  228 

Harmonic  modulation,  53 

Rule  I,  Tonic  for  new  Dominant,  54 

Rule  1 1,  Supertonic  for  new  Dominant,56 

Rule  III,  mediant  for  new  Dominant,  57 

Rule  IV,  Subdominant  for  new  Domi- 
nant, 59 

Rule  V,  submediant  for  new  Dominant, 
60 

Rule  VI,  subtonic  for  new  Dominant,  60 
Harmonization  of  melodies.  Rule  I,  66 

Rule  II,  first  of  the  scale  repeated,  69 

Rule  III,  fourth  of  the  scale  followed  by 
the  third,  69 

Rule  IV,  fifth  of  the  scale,  70 

Rule  V,  primary  note  followed  by  an- 
other a  fourth  higher,  73 

Rule  VI,  second  of  the  scale  with  sec- 
ondary Subdominant  chords,  86 

additional  rules,  165,  175,  219,  242 

by  three  primary  chords,  66 

Dominant  not  to  be  followed  by  Sub- 
dominant,  80 

employing  inversions,  with  diatonic  bass 
passages,  77 

initial,  final,  and  penultimate  chords  in 
fundamental  position,  80 

Imitation,  definition  of,  186 

in  two  voices,  187 

in  three  voices,  247 

over  given  fundamentals,  245 
Immediate  modulation,  203 
Incomplete  cadence,  191 
Indirectly  related  keys,  204 
Intervals,  definition  of,  7 

augmented,  10,  76 

computed  upward,  7 

consonant,  13 

diminished,  9 

dissonant,  14 

general  name  of,  7 

greater  than  the  octave,  7 

inversion  of,  12 

major,  7 

minor,  9 

perfect,  7 

specific  name  of,  7 
Inversion  of  chords,  24 
Irregular    resolution    of     the     Dominant 
seventh  chord,  258 

Keys,  directly  related,  63,  65 
extraneous,  203 


INDEX 


299 


foreign,  207 
indirectly  related,  204 

Leading  tone,  definition  of,  5 

Major  diatonic  scales,  2 
Major  intervals,  7 
Major  triad,  16 
Mediant,  definition  of,  4 
Mediant  seventh  chord,  271 
Melodic  modulation,  59,  93 

six  rules,  94-99 

additional  rule.  173 
Melody  over  indicated  bass,  31,  iSo 
Minor  scale,  definition  of,  3 

harmonic,  126 

melodic,  126 

normal,  4,  126 

relative,  3 

Tonic,  4 
Minor  triad,  16 

Modern  augmented  sixth  chord,  229 
Modulation,  definition  of,  53 

deferred,  203 

extraneous,  203 

harmonic,  53,  63 

immediate,  203 

passing,  73,  88,  175,  275 

serial,  53-62 
Modulation  scheme  for  chorals,  223 
Motion,  contrary,  20 

contrary,  to  avoid  faulty  parallels,  41 

oblique,  20 

similar,  20 
Motus,  definition  of,  132 

Neapolitan  sixth  chord,  234 
Nominal  fundamental,  80,  170 
Normal  minor  scale,  4,  126 
Notes,  definition  of,  i 

auxiliary,  136 

changing,  152 

common  to  two  chords,  20 

passing,  123 

primary.  5 

secondary,  5 

suitable  for  doubling,  19 

Oblique  motion,  20 

Open  (or  dispersed)  position,  28 

Optional  resolution,  45 

Organ  point,  290 

Ornamental  anticipation,  254 

Ornamental  resolution,  of  the  ninth,  168 

of  the  seventh,  258 

of  suspensions,  255 

Parallel  fifths  and  octaves,  40 

as  used  by  modern  composers,  41 
progressing  by  skip,  40 

Passing  cadence,  198 


Passing  modulation,  73,  88,  175,  219,  275 
Passing  notes,  definition  of,  123 

chromatic,  132 

compound,  129 

extended,  133 

repeated,  130 

successive,  124 
Pedal  point,  290 

double,  292 

inverted,  290 
Phrygian  cadence,  262 
Plagal  cadence,  194 
Primary  notes.  5 
Progression,  chromatic,  6 

faulty,  40,  105.  129 
Progression  of  voices,  19 

by  augmented  interval,  76 

by  degree,  19 

by  skip,  19 

chromatic,  19 

Real  fundamental,  80,  170 
Real  sequence,  287 
Relative  minor  scale,  3 
Resolution,  definition  of,  44 
compulsory,  44 
of    Dominant    added    sixth    chord    to 

Tonic,  271 
of    Dominant    added     sixth    chord    to 

Tonic  added  sixth  chord,  271 
of  Dominant  chords  to  Tonic  substituted 

sixth  chord,  21 1 
of  Dominant  chords  to  Tonic  added  sixth 

chord,  216 
of  Dominant  fifth,  45,  46.  162.  171,  172 
of  Dominant  seventh,  49,  227,  239,  243, 

-77 
of  Dominant  third,  44,  68,  213,  216 
of  Dominant  third  in  successive  Dom- 
inants, 74 
optional,  45 

Scale,  definition  of,  2 

harmQnic  minor,  126 

major  diatonic,  2 

melodic  minor,  126 

minor,  for  use  with  Tonic,  Subdominant, 
and  Dominant  chords,  128 

normal  minor,  4,  126 

relative  minor,  3 

rule  for  formation  of  signatures.  5 

technical  names  of  scale  members,  4 

Tonic  minor,  4 
Second  inversion  of  triads.  26 
Secondarj-  chords,  on  the  Dominant,  264 

on  the  Subdominant,  S3 

on  the  Tonic,  21 1 
Secondary  notes.  5 
Sensitive  tones,  44 
Sequences,  definition  of,  287 

real,  2S7 


300 


CUMULATIVE  HARMONY 


tonal,  287 

rules  for  tonal,  287 
Serial  modulations,  53 
Signatures,  5 
Similar  motion,  20 
Step  and  half  step,  definition  of,  i 
Subdominant,  definition  of,  4 
Subdominant  added  sixth  chord,  84 
Subdominant  ninth  chord,  282 
Subdominant  seventh  chord,  278 
Subdominant  substituted  sixth  chord,  83 
Subject  for  imitation,  185 
Submediant,  definition  of,  4 
Submediant  seventh  chord,  216 
Submediant  triad,  211 

Substituted  sixth  chord,  on  the  Dominant, 
264 

on  the  Subdominant,  83 

on  the  Tonic,  21 1 
Subtonic,  definition  of,  5 
Subtonic    triad    (abbreviated     Dominant), 

80 
Successive  Dominants,  74,  90 
Supertonic,  definition  of,  4 
Supertonic  seventh  chord,  84 
Supertonic  triad,  83 
Suspensions,  definition  of,  103 

double,  1 13 

of  chords,  120 

on  accented  part  of  bar,  105 

ornamentally  resolved,  255 


prepared,  sustained,  resolved,  103 
resolution  not  doubled,  105 
Rules  I,  II,  III,  IV,  106-110 

Table  of  chords  included  in  the  three  pri- 
mary families,  282 

Tierce  de  Picardie,  195 

Tonal  sequence,  definition  of,  287 
rules  for,  287 

Tones  common  to  two  chords,  20 

Tonic  added  sixth  chord,  216 

Tonic  minor  scale,  4 

Tonic  ninth  chord,  282 

Tonic  seventh  chord,  278 

Tonic  substituted  sixth  chord,  211 

Transition,  definition  of,  209 

Transposition,  definition  of,  21 

Triad,  definition  of,  16 
augmented,  17 
diminished,  17 
major,  16 
minor,  16 

Voices,  change  of  position  of,  33 
compass  of,  22 
difference  in  altitude  of,  22 
names  of,  19 
not  to  be  overlapped,  80 
progression  of,  19 

progression  by  augmented  intervals  to 
be  avoided,  76 


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